Acyclic coloring of two operations of graphs
Year: 2025
Type: conference-paper
Abstract: The coloring theory of graphs is a very important direction in graph theory. The graph coloring problem has a strong application background. Many practical problems such as timetabling problems, frequency allocation problems, traffic arrangements, circuit design, and storage problems can be transformed into graph coloring problems. A substantial amount of scholarly work has been dedicated to the exploration of acyclic coloring, resulting in a plethora of significant findings that significantly contribute to the theoretical framework of vertex coloring in graphs. An acyclic coloring of a graph G refers to a proper vertex coloring where the subgraph resulting from any pair of color classes does not encompass any cycles. We analyze acyclic coloring in splitting graphs and Cartesian products of paths and cycles by using the method of structural coloring, reductive proof, and mathematical induction. Moreover, we present the precise acyclic chromatic numbers for splitting graphs of cycles and Cartesian products of paths and cycles.
Authors: Xinze Jin, Shuangliang Tian
Institution: Northwest Minzu University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408039427