On independent star sets in finite graphs

Citation

Rowlinson P (2014) On independent star sets in finite graphs. Linear Algebra and Its Applications, 442, pp. 82-91. https://doi.org/10.1016/j.laa.2013.06.009

Abstract
Let G be a finite graph with μ as an eigenvalue of multiplicity k. A star set for μ is a set X of k vertices in G such that μ is not an eigenvalue of G-X. We investigate independent star sets of largest possible size in a variety of situations. We note connections with symmetric designs, codes, strongly regular graphs, and graphs with least eigenvalue -2.

Keywords
Eigenvalue; Error-correcting code; Star set; Strongly regular graph; Symmetric design

Journal
Linear Algebra and Its Applications: Volume 442

People

Professor Peter Rowlinson

Emeritus Professor, Mathematics