Elsevier, Linear Algebra and its Applications, (458), p. 149-160, 2014
DOI: 10.1016/j.laa.2014.06.011
Full text: Unavailable
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.