Bondage Numbers ofC4Bundles over a CycleCn

Moo Young Sohn,Fu-Tao Hu,Jaeun Lee

doi:10.1155/2013/520251

Moo Young Sohn, Fu-Tao Hu + Show 1 more

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https://doi.org/10.1155/2013/520251

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Abstract

Graph bundles generalize the notion of covering graphs and graph products. Graph bundles have been applied in computer architecture and communication networks. The bondage number is an important parameter for measuring the vulnerability and stability of the network domination under link failure. The bondage numberb(G)of a graphGis the minimum number of edges whose removal enlarges the domination number. In this paper, we show that the bondage number of everyC4bundles over a cycleCn (n≥4)is equal to 4.

Highlights

For notation and graph theoretical terminology not defined here, we follow [1]
Let G = (V, E) be an undirected graph without loops and multiedges, where V = V(G) is the vertex set and E = E(G) is the edge set, which is a subset of the set of all unordered pair of V
For any disjoint subset S, T ⊆ V, we denote [S, T] by the edge set between S and T of G

Summary

Introduction

For notation and graph theoretical terminology not defined here, we follow [1]. let G = (V, E) be an undirected graph without loops and multiedges, where V = V(G) is the vertex set and E = E(G) is the edge set, which is a subset of the set of all unordered pair of V. The domination number of G, denoted by γ(G), is the minimum cardinality among all dominating sets. A subset B of E(G) is called a bondage set of G if its removal from G results in a graph with larger domination number than γ(G).

Results

Conclusion