IJPAM: Volume 107, No. 3 (2016)

RESULTS ON DOMINATION NUMBER AND
BONDAGE NUMBER FOR SOME FAMILIES OF GRAPHS

G. Hemalatha$^1$, P. Jeyanthi$^2$
$^1$Department of Mathematics
Shri Andal Alagar College of Engineering
Mamandur, Kancheepuram, Tamil Nadu, INDIA
$^2$Research Centre, Department of Mathematics
Govindammal Aditanar College for Women
Tiruchendur 628 215, Tamil Nadu, INDIA


Abstract. Let $G =(V,E)$ be a simple graph on the vertex set $V$. In a graph $G$, A set $S\subseteq V$ is a dominating set of $G$ if every vertex in $V – S$ is adjacent to some vertex in $S$. The domination number of a graph $G \ga(G)]$ is the minimum size of a dominating set of vertices in $G$. The bondage number of a graph $G[Bd \ga(G)]$ is the cardinality of a smallest set of edges whose removal results in a graph with domination number larger than that of $G$. In this paper we establish domination number and the bondage number for some families of graphs.

Received: October 17, 2015

AMS Subject Classification: 05C69

Key Words and Phrases: dominating set, bondage number, domination number, cocktail party graph, coxeter graph, crown graph, cubic symmetric graph, doyle graph, folkman graph, levi graph, icosahedral graph

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DOI: 10.12732/ijpam.v107i3.5 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 107
Issue: 3
Pages: 565 - 577


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