Susana Clara López
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
Susana Clara López has a total of 27 co-authors. Here are the top co-authors by number of shared publications:
- Francesc-Antoni Muntaner-Batle
Graph Theory and Applications Research Group, School of Electrical Engineering and Computer Science, Faculty of Engineering and Built Environment, The University of Newcastle, NSW, 2308, Australia
20 shared publications - Anna Lladó
Department of Mathematics Universitat Politècnica de Catalunya Barcelona Spain
7 shared publications F.A. Muntaner-Batle
Graph Theory and Applications Research Group, School of Electrical Engineering and Computer Science, Faculty of Engineering and Built Environment, The University of Newcastle, NSW 2308, Australia
5 shared publications- Mohan Prabu
British University Vietnam, Hanoi, Vietnam
5 shared publications - Miquel Rius-Font
Universitat Politecnica de Catalunya
4 shared publications M. Rius-Font
3 shared publications
Latest Publications
- Open Access
- 1 January 2024
- Published by Georgia Southern University in Theory and Applications of Graphs
- Vol. 11 (1) , 1-11
Recent studies on the super edge-magic deficiency of graphs
A graph $G$ is called edge-magic if there exists a bijective function $f:V\left(G\right) \cup E\left(G\right)\rightarrow \left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert +\left\vert E\left(G\right) \right\vert \right\}$ such that $f\left(u\right) + f\left(v\right) + f\left(uv\right)$ is a constant for each $uv\in E\left( G\right) $. Also, $G$ is called super edge-magic if $f\left(V \left(G\right)\right) =\left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert \right\}$. Furthermore, the super edge-magic deficiency $ \mu_{s}\left(G\right)$ of a graph $G$ is defined to be either the smallest nonnegative integer $n$ with the property that $G \cup nK_{1}$ is super edge-magic or $+ \infty$ if there exists no such integer $n$. In this paper, we introduce the parameter $l\left(n\right)$ as the minimum size of a graph $G$ of order $n$ for which all graphs of order $n$ and size at least $l\left(n\right)$ have $\mu_{s} \left( G \right)=+\infty $, and provide lower and upper bounds for $l\left(n\right)$. Imran, Baig, and Fe\u{n}ov\u{c}\'{i}kov\'{a} established that for integers $n$ with $n\equiv 0\pmod{4}$, $ \mu_{s}\left(D_{n}\right) \leq 3n/2-1$, where $D_{n}$ is the cartesian product of the cycle $C_{n}$ of order $n$ and the complete graph $K_{2}$ of order $2$. We improve this bound by showing that $ \mu_{s}\left(D_{n}\right) \leq n+1$ when $n \geq 4$ is even. Enomoto, Llad\'{o}, Nakamigawa, and Ringel posed the conjecture that every nontrivial tree is super edge-magic. We propose a new approach to attack this conjecture. This approach may also help to resolve another labeling conjecture on trees by Graham and Sloane.- 1 January 2024
- Published by Georgia Southern University in Theory and Applications of Graphs
- Vol. 11 (1) , 1-11
Open AccessRecent studies on the super edge-magic deficiency of graphs
A graph $G$ is called edge-magic if there exists a bijective function $f:V\left(G\right) \cup E\left(G\right)\rightarrow \left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert +\left\vert E\left(G\right) \right\vert \right\}$ such that $f\left(u\right) + f\left(v\right) + f\left(uv\right)$ is a constant for each $uv\in E\left( G\right) $. Also, $G$ is called super edge-magic if $f\left(V \left(G\right)\right) =\left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert \right\}$. Furthermore, the super edge-magic deficiency $ \mu_{s}\left(G\right)$ of a graph $G$ is defined to be either the smallest nonnegative integer $n$ with the property that $G \cup nK_{1}$ is super edge-magic or $+ \infty$ if there exists no such integer $n$. In this paper, we introduce the parameter $l\left(n\right)$ as the minimum size of a graph $G$ of order $n$ for which all graphs of order $n$ and size at least $l\left(n\right)$ have $\mu_{s} \left( G \right)=+\infty $, and provide lower and upper bounds for $l\left(n\right)$. Imran, Baig, and Fe\u{n}ov\u{c}\'{i}kov\'{a} established that for integers $n$ with $n\equiv 0\pmod{4}$, $ \mu_{s}\left(D_{n}\right) \leq 3n/2-1$, where $D_{n}$ is the cartesian product of the cycle $C_{n}$ of order $n$ and the complete graph $K_{2}$ of order $2$. We improve this bound by showing that $ \mu_{s}\left(D_{n}\right) \leq n+1$ when $n \geq 4$ is even. Enomoto, Llad\'{o}, Nakamigawa, and Ringel posed the conjecture that every nontrivial tree is super edge-magic. We propose a new approach to attack this conjecture. This approach may also help to resolve another labeling conjecture on trees by Graham and Sloane. - Open Access
- 27 May 2021
- Published by Wiley in Mathematical Problems in Engineering
- Vol. 2021, 1-8
Distance-Based Topological Polynomials Associated with Zero-Divisor Graphs
Let be a commutative ring with nonzero identity and let be its set of zero divisors. The zero-divisor graph of is the graph with vertex set , where , and edge set . One of the basic results for these graphs is that is connected with diameter less than or equal to 3. In this paper, we obtain a few distance-based topological polynomials and indices of zero-divisor graph when the commutative ring is , namely, the Wiener index, the Hosoya polynomial, and the Shultz and the modified Shultz indices and polynomials.
- 27 May 2021
- Published by Wiley in Mathematical Problems in Engineering
- Vol. 2021, 1-8
Open AccessDistance-Based Topological Polynomials Associated with Zero-Divisor Graphs
Let be a commutative ring with nonzero identity and let be its set of zero divisors. The zero-divisor graph of is the graph with vertex set , where , and edge set . One of the basic results for these graphs is that is connected with diameter less than or equal to 3. In this paper, we obtain a few distance-based topological polynomials and indices of zero-divisor graph when the commutative ring is , namely, the Wiener index, the Hosoya polynomial, and the Shultz and the modified Shultz indices and polynomials.
- 22 October 2020
- Published by Springer Nature in Bulletin of the Malaysian Mathematical Sciences Society
- Vol. 44 (4) , 1881-1892
(Di)graph Decompositions and Magic Type Labelings: A Dual Relation
- 22 October 2020
- Published by Springer Nature in Bulletin of the Malaysian Mathematical Sciences Society
- Vol. 44 (4) , 1881-1892
(Di)graph Decompositions and Magic Type Labelings: A Dual Relation
- Open Access
- 8 February 2020
- Published by Springer Nature in Results in Mathematics
- Vol. 75 (1) , 1-13
New Constructions for the n-Queens Problem
- 8 February 2020
- Published by Springer Nature in Results in Mathematics
- Vol. 75 (1) , 1-13
Open AccessNew Constructions for the n-Queens Problem
- Open Access
New constructions for the $n$-queens problem
Let $D$ be a digraph, possibly with loops. A queen labeling of $D$ is a bijective function $l:V(G)\longrightarrow \{1,2,\ldots,|V(G)|\}$ such that, for every pair of arcs in $E(D)$, namely $(u,v)$ and $(u',v')$ we have (i) $l(u)+l(v)\neq l(u')+l(v')$ and (ii) $l(v)-l(u)\neq l(v')-l(u')$. Similarly, if the two conditions are satisfied modulo $n=|V(G)|$, we define a modular queen labeling. There is a bijection between (modular) queen labelings of $1$-regular digraphs and the solutions of the (modular) $n$-queens problem. The $\otimes_h$-product was introduced in 2008 as a generalization of the Kronecker product and since then, many relations among labelings have been established using the $\otimes_h$-product and some particular families of graphs. In this paper, we study some families of $1$-regular digraphs that admit (modular) queen labelings and present a new construction concerning to the (modular) $n$-queens problem in terms of the $\otimes_h$-product, which in some sense complements a previous result due to P\'olya.Open AccessNew constructions for the $n$-queens problem
Let $D$ be a digraph, possibly with loops. A queen labeling of $D$ is a bijective function $l:V(G)\longrightarrow \{1,2,\ldots,|V(G)|\}$ such that, for every pair of arcs in $E(D)$, namely $(u,v)$ and $(u',v')$ we have (i) $l(u)+l(v)\neq l(u')+l(v')$ and (ii) $l(v)-l(u)\neq l(v')-l(u')$. Similarly, if the two conditions are satisfied modulo $n=|V(G)|$, we define a modular queen labeling. There is a bijection between (modular) queen labelings of $1$-regular digraphs and the solutions of the (modular) $n$-queens problem. The $\otimes_h$-product was introduced in 2008 as a generalization of the Kronecker product and since then, many relations among labelings have been established using the $\otimes_h$-product and some particular families of graphs. In this paper, we study some families of $1$-regular digraphs that admit (modular) queen labelings and present a new construction concerning to the (modular) $n$-queens problem in terms of the $\otimes_h$-product, which in some sense complements a previous result due to P\'olya. - Open Access
(Di)graph decompositions and magic type labelings: a dual relation
A graph $G$ is called edge-magic if there is a bijective function $f$ from the set of vertices and edges to the set $\{1,2,\ldots,|V(G)|+|E(G)|\}$ such that the sum $f(x)+f(xy)+f(y)$ for any $xy$ in $E(G)$ is constant. Such a function is called an edge-magic labelling of G and the constant is called the valence of $f$. An edge-magic labelling with the extra property that $f(V(G))= \{1,2,\ldots,|V(G)|\}$ is called super edge-magic. In this paper, we establish a relationship between the valences of (super) edge-magic labelings of certain types of bipartite graphs and the existence of a particular type of decompositions of such graphs.Open Access(Di)graph decompositions and magic type labelings: a dual relation
A graph $G$ is called edge-magic if there is a bijective function $f$ from the set of vertices and edges to the set $\{1,2,\ldots,|V(G)|+|E(G)|\}$ such that the sum $f(x)+f(xy)+f(y)$ for any $xy$ in $E(G)$ is constant. Such a function is called an edge-magic labelling of G and the constant is called the valence of $f$. An edge-magic labelling with the extra property that $f(V(G))= \{1,2,\ldots,|V(G)|\}$ is called super edge-magic. In this paper, we establish a relationship between the valences of (super) edge-magic labelings of certain types of bipartite graphs and the existence of a particular type of decompositions of such graphs. - Open Access
Characterizing path-like trees from linear configurations
Assume that we embed the path $P_n$ as a subgraph of a $2$-dimensional grid, namely, $P_k \times P_l$. Given such an embedding, we consider the ordered set of subpaths $L_1, L_2, \ldots , L_m$ which are maximal straight segments in the embedding, and such that the end of $L_i$ is the beginning of $L_{i+1}$. Suppose that $L_i\cong P_2$, for some $i$ and that some vertex $u$ of $L_{i-1}$ is at distance $1$ in the grid to a vertex $v$ of $L_{i+1}$. An elementary transformation of the path consists in replacing the edge of $L_i$ by a new edge $uv$. A tree $T$ of order $n$ is said to be a path-like tree, when it can be obtained from some embedding of $P_n$ in the $2$-dimensional grid, by a sequence of elementary transformations. Thus, the maximum degree of a path-like tree is at most $4$. Intuitively speaking, a tree admits a linear configuration if it can be described by a sequence of paths in such a way that only vertices from two consecutive paths, which are at the same distance of the end vertices are adjacent. In this paper, we characterize path-like trees of maximum degree $3$, with an even number of vertices of degree $3$, from linear configurations.Open AccessCharacterizing path-like trees from linear configurations
Assume that we embed the path $P_n$ as a subgraph of a $2$-dimensional grid, namely, $P_k \times P_l$. Given such an embedding, we consider the ordered set of subpaths $L_1, L_2, \ldots , L_m$ which are maximal straight segments in the embedding, and such that the end of $L_i$ is the beginning of $L_{i+1}$. Suppose that $L_i\cong P_2$, for some $i$ and that some vertex $u$ of $L_{i-1}$ is at distance $1$ in the grid to a vertex $v$ of $L_{i+1}$. An elementary transformation of the path consists in replacing the edge of $L_i$ by a new edge $uv$. A tree $T$ of order $n$ is said to be a path-like tree, when it can be obtained from some embedding of $P_n$ in the $2$-dimensional grid, by a sequence of elementary transformations. Thus, the maximum degree of a path-like tree is at most $4$. Intuitively speaking, a tree admits a linear configuration if it can be described by a sequence of paths in such a way that only vertices from two consecutive paths, which are at the same distance of the end vertices are adjacent. In this paper, we characterize path-like trees of maximum degree $3$, with an even number of vertices of degree $3$, from linear configurations. - 1 August 2017
- Published by Elsevier in Discrete Mathematics
- Vol. 340 (8) , 1903-1909
A new labeling construction from the-product- 1 August 2017
- Published by Elsevier in Discrete Mathematics
- Vol. 340 (8) , 1903-1909
A new labeling construction from the-product- 1 July 2017
- Published by Elsevier in Electronic Notes in Discrete Mathematics
- Vol. 60, 55-60
(Di)graph products, labelings and related results
- 1 July 2017
- Published by Elsevier in Electronic Notes in Discrete Mathematics
- Vol. 60, 55-60
(Di)graph products, labelings and related results
- Open Access
On the super edge-magicness of graphs of equal order and size
The super edge-magicness of graphs of equal order and size has been shown to be important since such graphs can be used as seeds to answer many questions related to (super) edge-magic labelings and other types of well studied labelings, as for instance harmonious labelings. Also other questions related to the area of combinatorics can be attacked and understood from the point of view of super edge-magic graphs of equal order and size. For instance, the design of Steiner triple systems, the study of the set of dual shuffle primes and the Jacobsthal numbers. In this paper, we study the super edge-magic properties of some types of super edge-magic graphs of equal order and size, with the hope that they can be used later in the study of other related questions. The negative results found in last section are specially interesting since these kind of results are not common in the literature. Furthermore, the few results found in this direction usually meet one of the following reasons: too many vertices compared with the number of edges; too many edges compared with the number of vertices; or parity conditions. In this case, all previous reasons fail in our results.
Open AccessOn the super edge-magicness of graphs of equal order and size
The super edge-magicness of graphs of equal order and size has been shown to be important since such graphs can be used as seeds to answer many questions related to (super) edge-magic labelings and other types of well studied labelings, as for instance harmonious labelings. Also other questions related to the area of combinatorics can be attacked and understood from the point of view of super edge-magic graphs of equal order and size. For instance, the design of Steiner triple systems, the study of the set of dual shuffle primes and the Jacobsthal numbers. In this paper, we study the super edge-magic properties of some types of super edge-magic graphs of equal order and size, with the hope that they can be used later in the study of other related questions. The negative results found in last section are specially interesting since these kind of results are not common in the literature. Furthermore, the few results found in this direction usually meet one of the following reasons: too many vertices compared with the number of edges; too many edges compared with the number of vertices; or parity conditions. In this case, all previous reasons fail in our results.