Autor:	Lemańska, M., Swaminathan, V., Venkatakrishnan, Y. B., Zuazua, R.
Rok vydání:	2013
Předmět:	Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	Let $G=(V,E)$ be a graph. A subset $D$ of $V(G)$ is called a super dominating set if for every $v \in V(G)-D$ there exists an external private neighbour of $v$ with respect to $V(G)-D.$ The minimum cardinality of a super dominating set is called the super domination number of $G$ and is denoted by $\gamma_{sp}(G)$. In this paper some results on the super domination number are obtained. We prove that if $T$ is a tree with at least three vertices, then $\frac{n}{2}\leq\gamma_{sp}(T)\leq n-s,$ where $s$ is the number of support vertices in $T$ and we characterize the extremal trees. Comment: 7 pages, 4 references
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1309.1315 Zobrazit plný text záznamu View this record from Arxiv