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- W2168273587 abstract "Let $G=(V,E)$ be a graph, $Dsubseteq V(G)$ and $u$ be any vertex in $D$. The out degree of $u$ with respect to $D$ denoted by $ od_{_{D}}(u)$, is defined as $od_{_{D}}(u)=|N(u)D)|$. Let $G=(V,E)$ be a graph, $Dsubseteq V(G)$ and $u$ be any vertex in $D$. The out degree of $u$ with respect to $D$ denoted by $ od_{_{D}}(u)$, is defined as $od_{_{D}}(u)=|N(u)cap (V-D)|$. $D$ is called a near equitable dominating set of $G$ if for every $vin V-D$, there exists a vertex $uin D$ such that $u$ is adjacent to $v$ and $|od_{_D}(u)-od_{_{V-D}}(v)|leq 1$. The minimum cardinality of such a dominating set is denoted by $gamma_{ne}$ and is called the near equitable domination number of $G$. In this paper, we introduce the concept of near equitable domination. The minimal near equitable dominating sets are established. The relation between $gamma_{ne}(G)$, $gamma_{e}(G)$ and $gamma(G)$ are obtained, bounds for $gamma_{ne}(G)$ are found. Near equitable domatic partition in a graph $G$ is also studied." @default.
- W2168273587 created "2016-06-24" @default.
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- W2168273587 date "2014-05-28" @default.
- W2168273587 modified "2023-09-23" @default.
- W2168273587 title "On Near Equitable Domination in Graphs" @default.
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