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http://dx.doi.org/10.11568/kjm.2022.30.2.391

ON THE DOMINATION NUMBER OF A GRAPH AND ITS SQUARE GRAPH  

Murugan, E. (Department of Mathematics, Manonmaniam Sundaranar University)
Joseph, J. Paulraj (Department of Mathematics, Manonmaniam Sundaranar University)
Publication Information
Korean Journal of Mathematics / v.30, no.2, 2022 , pp. 391-402 More about this Journal
Abstract
For a given graph G = (V, E), a dominating set is a subset V' of the vertex set V so that each vertex in V ＼ V' is adjacent to a vertex in V'. The minimum cardinality of a dominating set of G is called the domination number of G and is denoted by γ(G). For an integer k ≥ 1, the k-th power Gk of a graph G with V (Gk) = V (G) for which uv ∈ E(Gk) if and only if 1 ≤ dG(u, v) ≤ k. Note that G2 is the square graph of a graph G. In this paper, we obtain some tight bounds for the sum of the domination numbers of a graph and its square graph in terms of the order, order and size, and maximum degree of the graph G. Also, we characterize such extremal graphs.
Keywords
domination number; square graph; order and size; planar graphs;
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Times Cited By KSCI : 1  (Citation Analysis)
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