The bondage number of graphs:good and bad vertices

Vladimir Samodivkin
<span title="">2008</span> <i title="Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Gora"> <a target="_blank" rel="noopener" href="" style="color: black;">Discussiones Mathematicae Graph Theory</a> </i> &nbsp;
The domination number γ(G) of a graph G is the minimum number of vertices in a set D such that every vertex of the graph is either in D or is adjacent to a member of D. Any dominating set D of a graph G with |D| = γ(G) is called a γ-set of G. A vertex x of a graph G is called: (i) γ-good if x belongs to some γ-set and (ii) γ-bad if x belongs to no γ-set. The bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with
more &raquo; ... tion number greater then γ(G). In this paper we present new sharp upper bounds for b(G) in terms of γ-good and γ-bad vertices of G.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.7151/dmgt.1419</a> <a target="_blank" rel="external noopener" href="">fatcat:awczdvixwfejnkl47zg6ykna24</a> </span>
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