Pedro García-Vázquez
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Pedro García-Vázquez has a total of 27 co-authors. Here are the top co-authors by number of shared publications:
C. Balbuena
18 shared publications- Martin Cera
Departamento de Matemática Aplicada I, Universidad de Sevilla ETS de Ingeniería informática, Avda. Reina Mercedes, s/n, 41012 Sevilla, Spain
18 shared publications - Juan Carlos Valenzuela-Tripodoro
Departamento de Matemáticas, Universidad de Cádiz, 11202 Algeciras, Spain
16 shared publications - Camino Balbuena
Departament de Matemática Aplicada III Universitat Politècnica de Catalunya Campus Nord Edifici C2 Girona 1 i 3 E-08034 Barcelona C Jordi Spain
13 shared publications X. Marcote
13 shared publications- Ana Diánez
Univ Seville, Dept Matemat Aplicada 1, E-41012 Seville, Spain
12 shared publications
Latest Publications
- Open Access
Strong Edge-Based Roman Domination in Fuzzy Graphs
This work is related to the extension of the well-known problem of Roman domination in graph theory to fuzzy graphs. A variety of approaches have been used to explore the concept of domination in fuzzy graphs. This study uses the concept of strong domination, considering the weights of the strong edges. We introduce the strong-neighbors Roman domination number of a fuzzy graph and establish some correlations with the Roman domination in graphs. The strong-neighbors Roman domination number is determined for specific fuzzy graphs, including complete and complete bipartite fuzzy graphs. Furthermore, several general bounds are given. In addition, we characterize the fuzzy graphs that reach the extreme values with particular attention to fuzzy strong cycles and paths.
Open AccessStrong Edge-Based Roman Domination in Fuzzy Graphs
This work is related to the extension of the well-known problem of Roman domination in graph theory to fuzzy graphs. A variety of approaches have been used to explore the concept of domination in fuzzy graphs. This study uses the concept of strong domination, considering the weights of the strong edges. We introduce the strong-neighbors Roman domination number of a fuzzy graph and establish some correlations with the Roman domination in graphs. The strong-neighbors Roman domination number is determined for specific fuzzy graphs, including complete and complete bipartite fuzzy graphs. Furthermore, several general bounds are given. In addition, we characterize the fuzzy graphs that reach the extreme values with particular attention to fuzzy strong cycles and paths.
- Open Access
- 31 July 2026
- Published by MDPI AG in Preprints.org
Positive-Influence via Roman Domination in Graphs
In this paper, we introduce and study the positive-influence Roman dominating function (PIRDF), a novel graph-theoretic concept that unifies Roman domination with positive-influence domination. A labeling f : V(G) → {0,1,2} is a PIRDF if it satisfies the Roman domination condition and the set of positively labeled vertices forms a positive-influence dominating set, meaning every unlabeled vertex has at least half of its neighbors positively labeled. The positive-influence Roman domination number, \( \gamma_R^{PI}(G) \), is defined as the minimum weight of a PIRDF of G. We establish several tight bounds. We prove that the associated decision problem is NP-complete for general graphs, and show that it is solvable in linear time for graph classes of bounded clique-width via a LinEMSOL1 formulation. Exact values of \( \gamma_R^{PI}(G) \) are computed for several standard graph families, including paths, cycles, complete graphs, complete bipartite graphs, star graphs, and friendship graphs. In addition, degree-based bounds are derived, and graphs attaining the lower bound \( \gamma_R^{PI}(G) = 1 + \lceil \delta/2 \rceil \) are fully characterized.- 31 July 2026
- Published by MDPI AG in Preprints.org
Open AccessPositive-Influence via Roman Domination in Graphs
In this paper, we introduce and study the positive-influence Roman dominating function (PIRDF), a novel graph-theoretic concept that unifies Roman domination with positive-influence domination. A labeling f : V(G) → {0,1,2} is a PIRDF if it satisfies the Roman domination condition and the set of positively labeled vertices forms a positive-influence dominating set, meaning every unlabeled vertex has at least half of its neighbors positively labeled. The positive-influence Roman domination number, \( \gamma_R^{PI}(G) \), is defined as the minimum weight of a PIRDF of G. We establish several tight bounds. We prove that the associated decision problem is NP-complete for general graphs, and show that it is solvable in linear time for graph classes of bounded clique-width via a LinEMSOL1 formulation. Exact values of \( \gamma_R^{PI}(G) \) are computed for several standard graph families, including paths, cycles, complete graphs, complete bipartite graphs, star graphs, and friendship graphs. In addition, degree-based bounds are derived, and graphs attaining the lower bound \( \gamma_R^{PI}(G) = 1 + \lceil \delta/2 \rceil \) are fully characterized. - Open Access
- 28 July 2026
- Published by MDPI AG in Preprints.org
Strong Edge-Based Roman Domination in Fuzzy Graphs
This work is related to the extension of the well-known problem of Roman domination in graph theory to fuzzy graphs. A variety of approaches have been used to explore the concept of domination in fuzzy graphs. This study uses the concept of strong domination, considering the weights of the strong edges. We introduce the strong-neighbors Roman domination number of a fuzzy graph and establish some correlations with the Roman domination in graphs. The strong-neighbors Roman domination number is determined for specific fuzzy graphs, including complete and complete bipartite fuzzy graphs. Besides, several general bounds are given. In addition, we characterize the fuzzy graphs that reach the extreme values with particular attention to fuzzy strong cycles and paths.
- 28 July 2026
- Published by MDPI AG in Preprints.org
Open AccessStrong Edge-Based Roman Domination in Fuzzy Graphs
This work is related to the extension of the well-known problem of Roman domination in graph theory to fuzzy graphs. A variety of approaches have been used to explore the concept of domination in fuzzy graphs. This study uses the concept of strong domination, considering the weights of the strong edges. We introduce the strong-neighbors Roman domination number of a fuzzy graph and establish some correlations with the Roman domination in graphs. The strong-neighbors Roman domination number is determined for specific fuzzy graphs, including complete and complete bipartite fuzzy graphs. Besides, several general bounds are given. In addition, we characterize the fuzzy graphs that reach the extreme values with particular attention to fuzzy strong cycles and paths.
- Open Access
Connectivity of Networks Modeled by Weighted Graphs
A graph together with two positive real-valued weight-functions and is called a weighted graph and is denoted by . In this paper, we introduce the concepts of connectivity, edge-connectivity, and restricted edge-connectivity for a weighted graph , and we prove general bounds analogous to those in the unweighted case. Furthermore, we study the connectivity and edge-connectivity of the line graph and the -path graph of a weighted graph, establishing upper and lower bounds for each of these parameters.Open AccessConnectivity of Networks Modeled by Weighted Graphs
A graph together with two positive real-valued weight-functions and is called a weighted graph and is denoted by . In this paper, we introduce the concepts of connectivity, edge-connectivity, and restricted edge-connectivity for a weighted graph , and we prove general bounds analogous to those in the unweighted case. Furthermore, we study the connectivity and edge-connectivity of the line graph and the -path graph of a weighted graph, establishing upper and lower bounds for each of these parameters. - Open Access
- 29 May 2026
- Published by MDPI AG in Preprints.org
Connectivity of Networks Modeled by Weighted Graphs
A graph G=(V,E) together with a positive real-valued weight-function w:V→R+ or w:E→R+ is called a weighted graph and is denoted by (G;w). In this paper, we introduce the concepts of connectivity, edge-connectivity, and restricted edge-connectivity for a weighted graph (G;w), and we prove general bounds analogous to those in the unweighted case. Furthermore, we study the connectivity and edge-connectivity of the line graph and the P2-path graph of a weighted graph, establishing upper and lower bounds for each of these parameters.
- 29 May 2026
- Published by MDPI AG in Preprints.org
Open AccessConnectivity of Networks Modeled by Weighted Graphs
A graph G=(V,E) together with a positive real-valued weight-function w:V→R+ or w:E→R+ is called a weighted graph and is denoted by (G;w). In this paper, we introduce the concepts of connectivity, edge-connectivity, and restricted edge-connectivity for a weighted graph (G;w), and we prove general bounds analogous to those in the unweighted case. Furthermore, we study the connectivity and edge-connectivity of the line graph and the P2-path graph of a weighted graph, establishing upper and lower bounds for each of these parameters.
- Open Access
- 29 January 2026
- Published by MDPI AG in Mathematics
- Vol. 14 (3) , 466
Roman Domination in Weighted Graphs
A Roman dominating function for a (non-weighted) graph is a function such that every vertex with has at least one neighbor such that . The minimum weight of a Roman dominating function f on G is called the Roman domination number of G and is denoted by . A graph , together with a positive real-valued weight-function , is called a weighted graph and is denoted by . The minimum weight of a Roman dominating function f on G is called the weighted Roman domination number of G and is denoted by . The domination and Roman domination numbers of unweighted graphs have been extensively studied, particularly for their applications in bioinformatics and computational biology. However, graphs used to model biomolecular structures often require weights to be biologically meaningful. In this paper, we initiate the study of the weighted Roman domination number in weighted graphs. We first establish several bounds for this parameter and present various realizability results. Furthermore, we determine the exact values for several well-known graph families and demonstrate an equivalence between the weighted Roman domination number and the differential of a weighted graph.- 29 January 2026
- Published by MDPI AG in Mathematics
- Vol. 14 (3) , 466
Open AccessRoman Domination in Weighted Graphs
A Roman dominating function for a (non-weighted) graph is a function such that every vertex with has at least one neighbor such that . The minimum weight of a Roman dominating function f on G is called the Roman domination number of G and is denoted by . A graph , together with a positive real-valued weight-function , is called a weighted graph and is denoted by . The minimum weight of a Roman dominating function f on G is called the weighted Roman domination number of G and is denoted by . The domination and Roman domination numbers of unweighted graphs have been extensively studied, particularly for their applications in bioinformatics and computational biology. However, graphs used to model biomolecular structures often require weights to be biologically meaningful. In this paper, we initiate the study of the weighted Roman domination number in weighted graphs. We first establish several bounds for this parameter and present various realizability results. Furthermore, we determine the exact values for several well-known graph families and demonstrate an equivalence between the weighted Roman domination number and the differential of a weighted graph. - Open Access
Roman domination in weighted graphs
A Roman dominating function for a (non-weighted) graph $G=(V,E)$, is a function $f:V\rightarrow \{0,1,2\}$ such that every vertex $u\in V$ with $f(u)=0$ has at least {one} neighbor $v\in V$ such that $f(v)=2$. The minimum weight $\sum_{v\in V}f(v)$ of a Roman {dominating function} $f$ on $G$ is called the Roman domination number of $G$ and is denoted by $γ_{R}(G)$. A graph {$G= (V,E)$} together with a positive real-valued weight-function $w:V\rightarrow \mathbf{R}^{>0}$ is called a {\it weighted graph} and is denoted by $(G;w)$. The minimum weight $\sum_{v\in V}f(v)w(v)$ of a Roman {dominating function} $f$ on $G$ is called the weighted Roman domination number of $G$ and is denoted by $γ_{wR}(G)$. The domination and Roman domination numbers of unweighted graphs have been extensively studied, particularly for their applications in bioinformatics and computational biology. However, graphs used to model biomolecular structures often require weights to be biologically meaningful. In this paper, we initiate the study of the weighted Roman domination number in weighted graphs. We first establish several bounds for this parameter and present various realizability results. Furthermore, we determine the exact values for several well-known graph families and demonstrate an equivalence between the weighted Roman domination number and the differential of a weighted graph.Open AccessRoman domination in weighted graphs
A Roman dominating function for a (non-weighted) graph $G=(V,E)$, is a function $f:V\rightarrow \{0,1,2\}$ such that every vertex $u\in V$ with $f(u)=0$ has at least {one} neighbor $v\in V$ such that $f(v)=2$. The minimum weight $\sum_{v\in V}f(v)$ of a Roman {dominating function} $f$ on $G$ is called the Roman domination number of $G$ and is denoted by $γ_{R}(G)$. A graph {$G= (V,E)$} together with a positive real-valued weight-function $w:V\rightarrow \mathbf{R}^{>0}$ is called a {\it weighted graph} and is denoted by $(G;w)$. The minimum weight $\sum_{v\in V}f(v)w(v)$ of a Roman {dominating function} $f$ on $G$ is called the weighted Roman domination number of $G$ and is denoted by $γ_{wR}(G)$. The domination and Roman domination numbers of unweighted graphs have been extensively studied, particularly for their applications in bioinformatics and computational biology. However, graphs used to model biomolecular structures often require weights to be biologically meaningful. In this paper, we initiate the study of the weighted Roman domination number in weighted graphs. We first establish several bounds for this parameter and present various realizability results. Furthermore, we determine the exact values for several well-known graph families and demonstrate an equivalence between the weighted Roman domination number and the differential of a weighted graph. - Open Access
- 23 December 2024
- Published by Springer Nature in Bulletin of the Malaysian Mathematical Sciences Society
- Vol. 48 (1) , 1-18
The k-Distance Mutual-Visibility Problem in Graphs
The concept of mutual visibility in graphs, introduced recently, addresses a fundamental problem in Graph Theory concerning the identification of the largest set of vertices in a graph such that any two vertices have a shortest path connecting them, excluding internal vertices of the set. Originally motivated by some challenges in Computer Science related to robot navigation, the problem seeks to ensure unobstructed communication channels between navigating entities. The mutual-visibility problem involves determining a largest mutual-visibility set in a graph. The mutual-visibility number of a graph represents the cardinality of the largest mutual-visibility set. This concept has sparked significant research interest, leading to connections with classical combinatorial problems like the Zarankiewicz problem and Turán-type problems. In this paper, we consider practical limitations in network visibility and our investigation extends the original concept to k-distance mutual-visibility. In this case, a pair of vertices is considered S-visible if a shortest path of length at most k exists, excluding internal vertices belonging to the set S. The k-distance mutual-visibility number represents the cardinality of a largest k-distance mutual-visibility set. We initiate the study of this new graph parameter. We prove that the associate decision problem belongs to the NP-complete class. We also give some properties and tight bounds, as well as, the exact value of such parameter for some particular non trivial graph classes.
- 23 December 2024
- Published by Springer Nature in Bulletin of the Malaysian Mathematical Sciences Society
- Vol. 48 (1) , 1-18
Open AccessThe k-Distance Mutual-Visibility Problem in Graphs
The concept of mutual visibility in graphs, introduced recently, addresses a fundamental problem in Graph Theory concerning the identification of the largest set of vertices in a graph such that any two vertices have a shortest path connecting them, excluding internal vertices of the set. Originally motivated by some challenges in Computer Science related to robot navigation, the problem seeks to ensure unobstructed communication channels between navigating entities. The mutual-visibility problem involves determining a largest mutual-visibility set in a graph. The mutual-visibility number of a graph represents the cardinality of the largest mutual-visibility set. This concept has sparked significant research interest, leading to connections with classical combinatorial problems like the Zarankiewicz problem and Turán-type problems. In this paper, we consider practical limitations in network visibility and our investigation extends the original concept to k-distance mutual-visibility. In this case, a pair of vertices is considered S-visible if a shortest path of length at most k exists, excluding internal vertices belonging to the set S. The k-distance mutual-visibility number represents the cardinality of a largest k-distance mutual-visibility set. We initiate the study of this new graph parameter. We prove that the associate decision problem belongs to the NP-complete class. We also give some properties and tight bounds, as well as, the exact value of such parameter for some particular non trivial graph classes.
- Open Access
The $k$-distance mutual-visibility problem in graphs
The concept of mutual visibility in graphs, introduced recently, addresses a fundamental problem in Graph Theory concerning the identification of the largest set of vertices in a graph such that any two vertices have a shortest path connecting them, excluding internal vertices of the set. Originally motivated by some challenges in Computer Science related to robot navigation, the problem seeks to ensure unobstructed communication channels between navigating entities. The mutual-visibility problem involves determining a largest mutual-visibility set in a graph. The mutual-visibility number of a graph represents the cardinality of the largest mutual-visibility set. This concept has sparked significant research interest, leading to connections with classical combinatorial problems like the Zarankiewicz problem and Turán-type problems. In this paper, we consider practical limitations in network visibility and our investigation extends the original concept to $k$-distance mutual-visibility. In this case, a pair of vertices is considered $S$-visible if a shortest path of length at most $k$ exists, excluding internal vertices belonging to the set $S$. The $k$-distance mutual-visibility number represents the cardinality of a largest $k$-distance mutual-visibility set. We initiate the study of this new graph parameter. We prove that the associate decision problem belongs to the NP-complete class. We also give some properties and tight bounds, as well as, the exact value of such parameter for some particular non trivial graph classes.Open AccessThe $k$-distance mutual-visibility problem in graphs
The concept of mutual visibility in graphs, introduced recently, addresses a fundamental problem in Graph Theory concerning the identification of the largest set of vertices in a graph such that any two vertices have a shortest path connecting them, excluding internal vertices of the set. Originally motivated by some challenges in Computer Science related to robot navigation, the problem seeks to ensure unobstructed communication channels between navigating entities. The mutual-visibility problem involves determining a largest mutual-visibility set in a graph. The mutual-visibility number of a graph represents the cardinality of the largest mutual-visibility set. This concept has sparked significant research interest, leading to connections with classical combinatorial problems like the Zarankiewicz problem and Turán-type problems. In this paper, we consider practical limitations in network visibility and our investigation extends the original concept to $k$-distance mutual-visibility. In this case, a pair of vertices is considered $S$-visible if a shortest path of length at most $k$ exists, excluding internal vertices belonging to the set $S$. The $k$-distance mutual-visibility number represents the cardinality of a largest $k$-distance mutual-visibility set. We initiate the study of this new graph parameter. We prove that the associate decision problem belongs to the NP-complete class. We also give some properties and tight bounds, as well as, the exact value of such parameter for some particular non trivial graph classes. - Open Access
- 1 January 2018
- Published by National Library of Serbia in Applicable Analysis and Discrete Mathematics
- Vol. 12 (2) , 297-317
On generalized 3-connectivity of the strong product of graphs
Let G be a connected graph with n vertices and let k be an integer such that 2 ? k ? n. The generalized connectivity kk(G) of G is the greatest positive integer l for which G contains at least l internally disjoint trees connecting S for any set S ? V (G) of k vertices. We focus on the generalized connectivity of the strong product G1 _ G2 of connected graphs G1 and G2 with at least three vertices and girth at least five, and we prove the sharp bound k3(G1 _ G2) ? k3(G1)_3(G2) + k3(G1) + k3(G2)-1.
- 1 January 2018
- Published by National Library of Serbia in Applicable Analysis and Discrete Mathematics
- Vol. 12 (2) , 297-317
Open AccessOn generalized 3-connectivity of the strong product of graphs
Let G be a connected graph with n vertices and let k be an integer such that 2 ? k ? n. The generalized connectivity kk(G) of G is the greatest positive integer l for which G contains at least l internally disjoint trees connecting S for any set S ? V (G) of k vertices. We focus on the generalized connectivity of the strong product G1 _ G2 of connected graphs G1 and G2 with at least three vertices and girth at least five, and we prove the sharp bound k3(G1 _ G2) ? k3(G1)_3(G2) + k3(G1) + k3(G2)-1.