Perfect r-Codes in Strong Products of Graphs
نویسندگان
چکیده
A perfect r-code in a graph is a subset of the graph’s vertices with the property that each vertex in the graph is within distance r of exactly one vertex in the subset. We prove that the n-fold strong product of simple graphs has a perfect r-code if and only if each factor has a perfect r-code.
منابع مشابه
Total perfect codes, OO-irredundant and total subdivision in graphs
Let $G=(V(G),E(G))$ be a graph, $gamma_t(G)$. Let $ooir(G)$ be the total domination and OO-irredundance number of $G$, respectively. A total dominating set $S$ of $G$ is called a $textit{total perfect code}$ if every vertex in $V(G)$ is adjacent to exactly one vertex of $S$. In this paper, we show that if $G$ has a total perfect code, then $gamma_t(G)=ooir(G)$. As a consequence, ...
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