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Hypo-efficient domination and hypo-unique domination
For a graph $G$ let $gamma (G)$ be its domination number. We define a graph G to be (i) a hypo-efficient domination graph (or a hypo-$mathcal{ED}$ graph) if $G$ has no efficient dominating set (EDS) but every graph formed by removing a single vertex from $G$ has at least one EDS, and (ii) a hypo-unique domination graph (a hypo-$mathcal{UD}$ graph) if $G$ has at least two minimum dominating sets...
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Let G be a connected graph of order n. A dominating set in G is a subset S of V(G) such that each element of V(G)− S is adjacent to a vertex of S. The least cardinality of a dominating set is the domination number. In the paper, we will give bounds of the Laplacian spectrum of G involving the domination number. © 2005 Elsevier Inc. All rights reserved. AMS classification: 05C50; 15A18
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2017
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-017-1844-x