total perfect codes, oo-irredundant and total subdivision in graphs
نویسندگان
چکیده
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, we determine the value of $ooir(g)$ for some classes of graphs.
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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عنوان ژورنال:
bulletin of the iranian mathematical societyجلد ۴۲، شماره ۳، صفحات ۴۹۹-۵۰۶
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