Co-cliques and star complements in extremal strongly regular graphs

Citation

Rowlinson P (2007) Co-cliques and star complements in extremal strongly regular graphs. Linear Algebra and Its Applications, 421 (1), pp. 157-162. https://doi.org/10.1016/j.laa.2006.04.002

Abstract
Suppose that the positive integer μ is the eigenvalue of largest multiplicity in an extremal strongly regular graph G. By interlacing, the independence number of G is at most 4μ2 + 4μ - 2. Star complements are used to show that if this bound is attained then either (a) μ = 1 and G is the Schläfli graph or (b) μ = 2 and G is the McLaughlin graph.

Keywords
graph; eigenvalue; star complement; independence number

Journal
Linear Algebra and Its Applications: Volume 421, Issue 1

People

Professor Peter Rowlinson

Emeritus Professor, Mathematics