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Elsevier, Linear Algebra and its Applications, (458), p. 149-160, 2014

DOI: 10.1016/j.laa.2014.06.011

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On bipartite graphs with complete bipartite star complements

Journal article published in 2014 by Peter Rowlinson
This paper was not found in any repository, but could be made available legally by the author.
This paper was not found in any repository, but could be made available legally by the author.

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Abstract

Let G be a bipartite graph with μ as an eigenvalue of multiplicity k>1k>1. We show that if G has Kr,sKr,s(1≤r≤s)(1≤r≤s) as a star complement for μ then k≤s-1k≤s-1; moreover if μ is non-main then k≤s-2k≤s-2 for large enough s . We provide examples of graphs in which various bounds on k or s are attained. We also describe the bipartite graphs with K1,sK1,s as a star complement for a non-main eigenvalue of multiplicity s-1>1s-1>1.