A Characterization of the Cactus Graphs with Equal Domination and Connected Domination Numbers
نویسنده
چکیده
A cactus graph is a connected graph in which any two cycles have at most one vertex in common. Let γ(G) and γc(G) be the domination number and connected domination number of a graph G, respectively. We can see that γ(G) ≤ γc(G) for any graph G. S. Arumugam and J. Paulraj Joseph [1] have characterized trees, unicyclic graphs and cubic graphs with equal domination and connected domination numbers. A few years later, Xue-gang Chena, Liang Suna, Hua-ming Xing [3] characterized the cactus graphs for which the domination number is equal to the connected domination number. Their characterization is in terms of global properties of a construction. In this paper, we provide a constructive characterization of the cactus graphs with equal domination and connected domination numbers. Mathematics Subject Classification: 05C69
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