Sogol Jahanbekam
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
Sogol Jahanbekam has a total of 37 co-authors. Here are the top co-authors by number of shared publications:
- Douglas B. West
Zhejiang Normal University, Jinhua, China
3 shared publications - Csaba Biró
Department of Mathematics, University of Louisville, Louisville, USA
2 shared publications - Daniel W. Cranston
Department of Mathematics William & Mary Williamsburg VA USA
2 shared publications Douglas B. West
2 shared publications- Emilyn Green
San José State University Department of Mathematics and Statistics San José, CA 95192
2 shared publications M. Ghanbari
Department of Mathematical Sciences, Sharif University of Technology, Iran
2 shared publications
Latest Publications
- 24 February 2024
- Published by Springer Nature in Graphs and Combinatorics
- Vol. 40 (2) , 1-15
Weak Dynamic Coloring of Planar Graphs
- 24 February 2024
- Published by Springer Nature in Graphs and Combinatorics
- Vol. 40 (2) , 1-15
Weak Dynamic Coloring of Planar Graphs
- 6 December 2021
- Published by Wiley in Journal of Mechanical Design
- Vol. 144 (5)
A Graph Partitioning Technique to Optimize the Physical Integration of Functional Requirements for Axiomatic Design
According to the concept of physical integration as understood in axiomatic design, design parameters of a product should be integrated into a single physical part or a few parts with the aim of reducing the information content, while still satisfying the independence of functional requirement. However, no specific method is suggested in the literature for determining the optimal degree of physical integration in a given design. This is particularly important with the current advancement in technologies such as additive manufacturing. As new manufacturing technologies allow physical elements to be integrated in new ways, new methods are needed to help designers optimize physical integration given the specific constraints and conflicts of each design. This study proposes an algorithm that uses graph partitioning to allow a designer to optimize the integration of functional requirements into a target number of parts, with the goal of minimizing the co-allocation of incompatible functional requirements in the same part. The operation and viability of the algorithm are demonstrated via two numerical examples and a practical example of designing a pencil.
- 6 December 2021
- Published by Wiley in Journal of Mechanical Design
- Vol. 144 (5)
A Graph Partitioning Technique to Optimize the Physical Integration of Functional Requirements for Axiomatic Design
According to the concept of physical integration as understood in axiomatic design, design parameters of a product should be integrated into a single physical part or a few parts with the aim of reducing the information content, while still satisfying the independence of functional requirement. However, no specific method is suggested in the literature for determining the optimal degree of physical integration in a given design. This is particularly important with the current advancement in technologies such as additive manufacturing. As new manufacturing technologies allow physical elements to be integrated in new ways, new methods are needed to help designers optimize physical integration given the specific constraints and conflicts of each design. This study proposes an algorithm that uses graph partitioning to allow a designer to optimize the integration of functional requirements into a target number of parts, with the goal of minimizing the co-allocation of incompatible functional requirements in the same part. The operation and viability of the algorithm are demonstrated via two numerical examples and a practical example of designing a pencil.
- Open Access
- 16 July 2021
- Published by ASME International
Design for Flexibility: A Graph Coloring Technique to Study Design Changes in the Tethered Economy World
Digitization, connected networks, embedded software, and smart devices have resulted in a major paradigm shift in business models. Transformative service-based business models are dominating the market, where advancement in technology has paved the way for offering not only a set of new services but also altering product functionalities and services over time. This paradigm shift
- 16 July 2021
- Published by ASME International
Open AccessDesign for Flexibility: A Graph Coloring Technique to Study Design Changes in the Tethered Economy World
Digitization, connected networks, embedded software, and smart devices have resulted in a major paradigm shift in business models. Transformative service-based business models are dominating the market, where advancement in technology has paved the way for offering not only a set of new services but also altering product functionalities and services over time. This paradigm shift
- 1 July 2021
- Published by Elsevier in Discrete Applied Mathematics
- Vol. 298, 80-83
Improved algorithm to determine 3-colorability of graphs with minimum degree at least 7
- 1 July 2021
- Published by Elsevier in Discrete Applied Mathematics
- Vol. 298, 80-83
Improved algorithm to determine 3-colorability of graphs with minimum degree at least 7
- 18 August 2019
- Published by ASME International
A Graph Coloring Technique for Identifying the Minimum Number of Parts for Physical Integration in Product Design
The objective of this study is to develop a mathematical framework for determining the minimum number of parts required in a product to satisfy a list of functional requirements (FRs) given a set of connections between FRs. The problem is modeled as a graph coloring technique in which a graph G with n nodes (representing the FRs) and m edges (representing the connections between the FRs) is studied to determine the graph’s chromatic number χ(G), which is the minimum number of colors required to properly color the graph. The chromatic number of the graph represents the minimum number of parts needed to satisfy the list of FRs. In addition, the study calculates the computational efficiency of the proposed algorithm. Several examples are provided to show the application of the proposed algorithm.
- 18 August 2019
- Published by ASME International
A Graph Coloring Technique for Identifying the Minimum Number of Parts for Physical Integration in Product Design
The objective of this study is to develop a mathematical framework for determining the minimum number of parts required in a product to satisfy a list of functional requirements (FRs) given a set of connections between FRs. The problem is modeled as a graph coloring technique in which a graph G with n nodes (representing the FRs) and m edges (representing the connections between the FRs) is studied to determine the graph’s chromatic number χ(G), which is the minimum number of colors required to properly color the graph. The chromatic number of the graph represents the minimum number of parts needed to satisfy the list of FRs. In addition, the study calculates the computational efficiency of the proposed algorithm. Several examples are provided to show the application of the proposed algorithm.
- 1 July 2019
- Published by Elsevier in Discrete Mathematics
- Vol. 342 (7) , 2012-2022
List-distinguishing Cartesian products of cliques
- 1 July 2019
- Published by Elsevier in Discrete Mathematics
- Vol. 342 (7) , 2012-2022
List-distinguishing Cartesian products of cliques
- 26 August 2018
- Published by ASME International
Graph Partitioning Technique to Identify Physically Integrated Design Concepts
This study proposes a graph partitioning method to facilitate the idea of physical integration proposed in Axiomatic Design. According to the physical integration concept, the design features should be integrated into a single physical part or a few parts with the aim of reducing the information content, given that the independence of functional requirements is still satisfied. However, no specific method is suggested in the literature for determining the optimal degree of physical integration of a design artifact. This is particularly important with the current advancement in Additive Manufacturing technologies. Since additive manufacturing allows physical elements to be integrated, new methods are needed to help designers evaluate the impact of the physical integration on the design success. The objective of this paper is to develop a framework for determining the best way that functional requirements can be assigned to different parts of a product.
- 26 August 2018
- Published by ASME International
Graph Partitioning Technique to Identify Physically Integrated Design Concepts
This study proposes a graph partitioning method to facilitate the idea of physical integration proposed in Axiomatic Design. According to the physical integration concept, the design features should be integrated into a single physical part or a few parts with the aim of reducing the information content, given that the independence of functional requirements is still satisfied. However, no specific method is suggested in the literature for determining the optimal degree of physical integration of a design artifact. This is particularly important with the current advancement in Additive Manufacturing technologies. Since additive manufacturing allows physical elements to be integrated, new methods are needed to help designers evaluate the impact of the physical integration on the design success. The objective of this paper is to develop a framework for determining the best way that functional requirements can be assigned to different parts of a product.
- Open Access
- 12 July 2018
- Published by The Electronic Journal of Combinatorics in The Electronic Journal of Combinatorics
- Vol. 25 (3) , P3.18
On the Strong Chromatic Index of Sparse Graphs
The strong chromatic index of a graph $G$, denoted $\chi'_s(G)$, is the least number of colors needed to edge-color $G$ so that edges at distance at most two receive distinct colors. The strong list chromatic index, denoted $\chi'_{s,\ell}(G)$, is the least integer $k$ such that if arbitrary lists of size $k$ are assigned to each edge then $G$ can be edge-colored from those lists where edges at distance at most two receive distinct colors.We use the discharging method, the Combinatorial Nullstellensatz, and computation to show that if $G$ is a subcubic planar graph with ${\rm girth}(G) \geq 41$ then $\chi'_{s,\ell}(G) \leq 5$, answering a question of Borodin and Ivanova [Precise upper bound for the strong edge chromatic number of sparse planar graphs, Discuss. Math. Graph Theory, 33(4), (2014) 759--770]. We further show that if $G$ is a subcubic planar graph and ${\rm girth}(G) \geq 30$, then $\chi_s'(G) \leq 5$, improving a bound from the same paper.Finally, if $G$ is a planar graph with maximum degree at most four and ${\rm girth}(G) \geq 28$, then $\chi'_s(G)N \leq 7$, improving a more general bound of Wang and Zhao from [Odd graphs and its applications to the strong edge coloring, Applied Mathematics and Computation, 325 (2018), 246-251] in this case.- 12 July 2018
- Published by The Electronic Journal of Combinatorics in The Electronic Journal of Combinatorics
- Vol. 25 (3) , P3.18
Open AccessOn the Strong Chromatic Index of Sparse Graphs
The strong chromatic index of a graph $G$, denoted $\chi'_s(G)$, is the least number of colors needed to edge-color $G$ so that edges at distance at most two receive distinct colors. The strong list chromatic index, denoted $\chi'_{s,\ell}(G)$, is the least integer $k$ such that if arbitrary lists of size $k$ are assigned to each edge then $G$ can be edge-colored from those lists where edges at distance at most two receive distinct colors.We use the discharging method, the Combinatorial Nullstellensatz, and computation to show that if $G$ is a subcubic planar graph with ${\rm girth}(G) \geq 41$ then $\chi'_{s,\ell}(G) \leq 5$, answering a question of Borodin and Ivanova [Precise upper bound for the strong edge chromatic number of sparse planar graphs, Discuss. Math. Graph Theory, 33(4), (2014) 759--770]. We further show that if $G$ is a subcubic planar graph and ${\rm girth}(G) \geq 30$, then $\chi_s'(G) \leq 5$, improving a bound from the same paper.Finally, if $G$ is a planar graph with maximum degree at most four and ${\rm girth}(G) \geq 28$, then $\chi'_s(G)N \leq 7$, improving a more general bound of Wang and Zhao from [Odd graphs and its applications to the strong edge coloring, Applied Mathematics and Computation, 325 (2018), 246-251] in this case. - 1 June 2016
- Published by Elsevier in Discrete Applied Mathematics
- Vol. 206, 65-72
On -dynamic coloring of graphs- 1 June 2016
- Published by Elsevier in Discrete Applied Mathematics
- Vol. 206, 65-72
On -dynamic coloring of graphs- Open Access
- 26 June 2015
- Published by Wiley in Journal of Graph Theory
- Vol. 82 (1) , 75-89
Anti‐Ramsey Problems for t Edge‐Disjoint Rainbow Spanning Subgraphs: Cycles, Matchings, or Trees
We seek the maximum number of colors in an edge‐coloring of the complete graph not having t edge‐disjoint rainbow spanning subgraphs of specified types. Let , , and denote the answers when the spanning subgraphs are cycles, matchings, or trees, respectively. We prove for and for . We prove for and for . We also provide constructions for the more general problem in which colorings are restricted so that colors do not appear on more than q edges at a vertex.
- 26 June 2015
- Published by Wiley in Journal of Graph Theory
- Vol. 82 (1) , 75-89
Open AccessAnti‐Ramsey Problems for t Edge‐Disjoint Rainbow Spanning Subgraphs: Cycles, Matchings, or Trees
We seek the maximum number of colors in an edge‐coloring of the complete graph not having t edge‐disjoint rainbow spanning subgraphs of specified types. Let , , and denote the answers when the spanning subgraphs are cycles, matchings, or trees, respectively. We prove for and for . We prove for and for . We also provide constructions for the more general problem in which colorings are restricted so that colors do not appear on more than q edges at a vertex.