Abstract

A $k$-coupon coloring of a graph $G$ without isolated vertices is an assignment of colors from $[k]=\{1,2,\hdots ,k\}$ to the vertices of $G$ such that the neighborhood of every vertex of $G$ contains vertices of all colors from $[k]$. The maximum $k$ for which a $k$-coupon coloring exists is called the coupon coloring number of $G$. In this paper, we have studied the coupon coloring number of ideal-based zero-divisor graphs of finite commutative rings.

Keywords and Phrases

Coupon coloring number, Total domatic number, Ideal-based zero-divisor graph.

A.M.S. subject classification

05C15, 05C25, 05C69.

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