Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4602202 | Linear Algebra and its Applications | 2009 | 7 Pages |
Abstract
In this paper we study graphs all of whose star sets induce cliques or co-cliques. We show that the star sets of every tree for each eigenvalue are independent sets. Among other results it is shown that each star set of a connected graph G with three distinct eigenvalues induces a clique if and only if G=K1,2 or K2,…,2. It is also proved that stars are the only graphs with three distinct eigenvalues having a star partition with independent star sets.
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Physical Sciences and Engineering
Mathematics
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