adjacent vertex distinguishing acyclic edge coloring of the cartesian product of graphs
نویسندگان
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 $chi^{prime}_{aa}(gsquare h)$ 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 $chi^{prime}_{aa}(c_msquare c_n)$ is at most $6$ fo every $mgeq 3$ and $ngeq 3$. moreover in some cases we find the exact value of $chi^{prime}_{aa}(c_msquare c_n)$.
منابع مشابه
Adjacent Vertex Distinguishing Acyclic Edge Coloring of the Cartesian Product of Graphs
Let G be a graph and χaa(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 χaa(G□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, C...
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عنوان ژورنال:
transactions on combinatoricsجلد ۶، شماره ۲، صفحات ۱۹-۳۰
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