In collaboration with Payame Noor University and the Iranian Society of Instrumentation and Control Engineers
Control and Optimization
A Hybrid Floyd-Warshall and Graph Coloring Algorithm for Finding the Smallest Number of Colors Needed for a Distance Coloring of Graphs

Hanifa Mosawi; Mostafa Tavakolli; Khatere Ghorbani-Moghadam

Volume 9, Issue 1 , May 2024, , Pages 185-194

  Graph coloring is a crucial area of research in graph theory, with numerous algorithms proposed for various types of graph coloring, particularly graph p-distance coloring‎. In this study, we employ a recently introduced graph coloring algorithm to develop a hybrid algorithm approximating the chromatic ...  Read More

The Smallest Number of Colors Needed for a‎ ‎Coloring of the Square of the Cartesian Product of Certain Graphs

Sajad Sohrabi Hesan; Freydoon Rahbarnia; Mostafa Tavakolli

Volume 8, Issue 1 , June 2023, , Pages 83-93

  Given any graph G‎, ‎its square graph G^2 has the same vertex set as G, ‎with two vertices adjacent in G^2 whenever they are at distance 1 or 2 in G. ‎‎The Cartesian product of graphs G and H is denoted by G□ H. ‎‎One of the most studied NP-hard problems is the graph coloring ...  Read More

Global Forcing Number for Maximal Matchings under Graph Operations

Mostafa Tavakolli

Volume 4, Issue 1 , July 2019, , Pages 53-63

  Let $S= \{e_1,\,e_2‎, ‎\ldots,\,e_m\}$ be an ordered subset of edges of a connected graph $G$‎. ‎The edge $S$-representation of an edge set $M\subseteq E(G)$ with respect to $S$ is the‎ ‎vector $r_e(M|S) = (d_1,\,d_2,\ldots,\,d_m)$‎, ‎where $d_i=1$ if $e_i\in M$ and $d_i=0$‎ ...  Read More