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  • Bondage number of grid graphs

    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 domination number greater than the domination number of G. Here we study the bondage number of some grid-like graphs. In this sense, we obtain some bounds or exact values of the bondage number of some strong product and direct product of two paths.

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  • Total Domination Versus Domination in Cubic Graphs

    A dominating set in a graph G is a set S of vertices of G such that every vertex not in S has a neighbor in S. Further, if every vertex of G has a neighbor in S, then S is a total dominating set of G. The domination number,γ(G), and total domination number, γ_t(G), are the minimum cardinalities of a dominating set and total dominating set, respectively, in G. The upper domination number, \Gamma(G), and the upper total domination...

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  • TOTAL DOMINATION MULTISUBDIVISION NUMBER OF A GRAPH

    - Discussiones Mathematicae Graph Theory - 2015

    The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G. Similarly we define the total domination multisubdivision number msd_t (G) of a graph G and we show that for any connected graph G of order at least two, msd_t (G) ≤ 3. We show that for trees the total domination...

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