On the nullity number of graphs

Mustapha Aouchiche, Pierre Hansen

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

The paper discusses bounds on the nullity number of graphs. It is proved in [B. Cheng and B. Liu, On the nullity of graphs. Electron. J. Linear Algebra 16 (2007) 60-67] that η ≤ n-D, where η, n and D denote the nullity number, the order and the diameter of a connected graph, respectively. We first give a necessary condition on the extremal graphs corresponding to that bound, and then we strengthen the bound itself using the maximum clique number. In addition, we prove bounds on the nullity using the number of pendant neighbors in a graph. One of those bounds is an improvement of a known bound involving the domination number.

Original languageEnglish
Pages (from-to)335-346
Number of pages12
JournalElectronic Journal of Graph Theory and Applications
Volume5
Issue number2
DOIs
Publication statusPublished - 2017
Externally publishedYes

Keywords

  • Adjacency matrix
  • Diameter
  • Domination number
  • Matching number
  • Nullity number
  • Pendant neighbor

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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