THE SUBSTANTIAL INDEPENDENCE NUMBER FOR THE GENERALIZED PETERSON GRAPH.
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Abstract
Given a graph G, a substantial independent set S is a subset of the vertices G which satisfies the conditions namely, S is an independent set of G and more over every vertex in V\S is adjacent to at most one vertex in S. The substantial independence number  is the maximum cardinality of a maximal substantial independent set S of G. In this paper we study the substantial independence number for the generalized Petersen graphs, by finding both sharp bounds and exact results for the Generalized Peterson Graphs.
 AMS No.: 05C69
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