Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416195 | Linear Algebra and its Applications | 2016 | 10 Pages |
Abstract
Let G be a connected triangle-free graph of order n>5 with μâ{â1,0} as an eigenvalue of multiplicity k>1. We show that if d is the maximum degree in G then kâ¤nâdâ1; moreover, if k=nâdâ1 then either (a) G is non-bipartite and kâ¤(μ2+3μ+1)(μ2+2μâ1), with equality only if G is strongly regular, or (b) G is bipartite and kâ¤dâ1, with equality only if G is a bipolar cone. In each case we discuss the extremal graphs that arise.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Peter Rowlinson,