Partition of a Graph with its Complete Sub-graphs

Prasad, Manjunath K and Sudhakara, G and Sujatha, H S (2012) Partition of a Graph with its Complete Sub-graphs. Advances and Applications in Discrete Mathematics, 10 (1). pp. 1-22. ISSN 0974-1658

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Abstract

A fundamental result regarding characterization of a bipartite graph is \vertex set V of a graph can be partitioned into two subsets of vertices V1 and V2 such that no two vertices from same set are at distance one (bipartite graph) if and only if given graph has no cycle of odd length". In this paper, we consider the class of all graphs with a partition for the set vertices, if exists, such that no two vertices from same set are at distance two (call it a (2; 2) bipartite graph) and obtain a characterization for such graphs. This characterization reveals that each set in the partition has sub partitions such that each set in the sub partition induces complete sub graphs and this result has signi�cance in providing a stable network. Also, analogue to the observation that a cycle (whenever exists) is of even length in the case of a bipartite graph, here in the case of (2; 2) bipartite graph, we �nd that an induced cycle, if exists, is a triangle or of length 4k, for some integer k.

Item Type: Article
Uncontrolled Keywords: Bipartite graph, Bipartition, Induced complete sub graph
Subjects: Departments at MU > Statistics
Engineering > MIT Manipal > Mathematics
Depositing User: MIT Library
Date Deposited: 16 Feb 2013 04:12
Last Modified: 16 Feb 2013 04:12
URI: http://eprints.manipal.edu/id/eprint/78437

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