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Journal of Algebraic Combinatorics

, Volume 47, Issue 1, pp 39–50 | Cite as

A graph for which the inertia bound is not tight

  • John SinkovicEmail author
Article
  • 172 Downloads

Abstract

The inertia bound gives an upper bound on the independence number of a graph by considering the inertia of matrices corresponding to the graph. The bound is known to be tight for graphs on 10 or fewer vertices as well as for all perfect graphs. It is natural to question whether the bound is always tight. We show that the bound is not tight for the Paley graph on 17 vertices as well as its induced subgraph on 16 vertices.

Keywords

Inertia bound Cvetković bound Independence number Weight matrix 

Mathematics Subject Classification

05C50 05C69 15A42 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

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