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Adjacent vertex distinguishing acyclic edge coloring of the Cartesian product of graphs | ||
| Transactions on Combinatorics | ||
| مقاله 7، دوره 6، شماره 2، تابستان 2017، صفحه 19-30 اصل مقاله (495.24 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2017.20988 | ||
| نویسندگان | ||
Fatemeh Sadat Mousavi  ؛ Massomeh Noori
| ||
| University of Zanjan | ||
| چکیده | ||
| 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 $\chi^{\prime}_{aa}(C_m\square C_n)$. | ||
| کلیدواژه‌ها | ||
| Acyclic edge coloring؛ adjacent vertex distinguishing acyclic edge coloring؛ adjacent vertex distinguishing acyclic edge chromatic number | ||
| مراجع | ||
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[8] Z. F. Zhang, L. Z. Liu and J. F. Wang, Adjacent strong edge coloring of graphs, Appl. Math. Lett., 15 (2002) 623-626. | ||
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