On Integrity of Harary Graphs

Authors:
Fengwei Li;Qingfang Ye;Baohuai Sheng
Affiliations:
Department of mathematics, Shaoxing University, Zhejiang, China 312000;Department of mathematics, Shaoxing University, Zhejiang, China 312000;Department of mathematics, Shaoxing University, Zhejiang, China 312000
Venue:
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Year:
2009

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Abstract

The integrity of a graph G = (V ,E ) is defined as I (G ) = min {|S | + m (G *** S ):S *** V (G )}, where m (G *** X ) denotes the order of the largest component in the graph G *** X . This is a better parameter to measure the stability of a network G , as it takes into account both the amount of work done to damage the network and how badly the network is damaged. In this paper, we give the exact values or bounds for the integrity of Harary graphs.