Adjacent vertex distinguishing acyclic edge coloring of the Cartesian product of graphs
نویسندگان
1 University of Zanjan
2 University of Zanjan
doi
10.22108/toc.2017.20988چکیده
Let $G$ be a graph and $\chi^{\prime}_{aa}(G)$ denotes the minimum number of colors required for an acyclic edge coloring of $G$ in which no two adjacent vertices are incident to edges colored with the same set of colors. We prove a general bound for $\chi^{\prime}_{aa}(G\square H)$ for any two graphs $G$ and $H$. We also determine exact value of this parameter for the Cartesian product of two paths, Cartesian product of a path and a cycle, Cartesian product of two trees, hypercubes. We show that $\chi^{\prime}_{aa}(C_m\square C_n)$ is at most $6$ fo every $m\geq 3$ and $n\geq 3$. Moreover in some cases we find the exact value of $\chi^{\prime}_{aa}(C_m\square C_n)$.
