Domination Numbers of Amalgamations of Cycles at Connected Subgraphs. (28th January 2022) - Boonmee, Prakassawat; Ma - In, Jirapa; Panma, Sayan
Abstract : A set S of vertices of a graph G is a dominating set of G if every vertex in V G is adjacent to some vertex in S . A minimum dominating set in a graph G is a dominating set of minimum cardinality. The cardinality of a minimum dominating set is called the domination number of G and is denoted by γ G . Let G 1 and G 2 be disjoint graphs, H 1 be a subgraph of G 1, H 2 be a subgraph of G 2, and f be an isomorphism from H 1 to H 2 . The amalgamation (the glued graph) of G 1 and G 2 at H 1 and H 2 with respect to f is the graph G = G 1 ⊲ ⊳ G 2 H 1 ≅ f H 2 obtained by forming the disjoint union of G 1 and G 2 and then identifying H 1 and H 2 with respect to f . In this paper, we determine the domination numbers of the amalgamations of two cycles at connected subgraphs.