Domination Numbers of Amalgamations of Cycles at Connected Subgraphs

Author:

Boonmee Prakassawat1ORCID,Ma - In Jirapa2ORCID,Panma Sayan23ORCID

Affiliation:

1. Department of Mathematics, Faculty of Science and Technology, Muban Chom Bueng Rajabhat University, Chom Bueng, Ratchaburi, Thailand

2. Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand

3. Advanced Research Center for Computational Simulation, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand

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.

Funder

Chiang Mai University

Publisher

Hindawi Limited

Subject

General Mathematics

Reference19 articles.

1. Theory of graphs;O. Ore;American Mathematical Society,1962

2. Towards a theory of domination in graphs

3. On the domination number of some graphs;S. Alikhani;International Mathematical Forum,2008

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