The bondage number of $C_3 \times C_n$

Moo Young Sohn; Yuan Xudong; Hyeon Seok Jeong

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2007; 44(6): 1213-1231

Printed November 1, 2007

The bondage number of $C_3 \times C_n$

Moo Young Sohn, Yuan Xudong, and Hyeon Seok Jeong

Changwon National University, Guangxi Normal University, Changwon National University

Abstract

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Abstract

The domination number $\gamma(G)$ of a graph $G = (V, E)$ is the minimum cardinality of a subset of $V$ such that every vertex is either in the set or is adjacent to some vertex in the set. The bondage number of $b(G)$ of a graph $G$ is the cardinality of a smallest set of edges whose removal from $G$ results in a graph with domination number greater than $\gamma(G)$. In this paper, we calculate the bondage number of the Cartesian product of cycles $C_3$ and $C_n$ for all $n $.

Keywords: graph, domination number, bondage number

MSC numbers: 05C50, 05C69