Loading...

On graphs whose star sets are (co-)cliques

Akbari, S ; Sharif University of Technology

166 Viewed
  1. Type of Document: Article
  2. DOI: 10.1016/j.laa.2008.08.013
  3. Abstract:
  4. In this paper we study graphs all of whose star sets induce cliques or co-cliques. We show that the star sets of every tree for each eigenvalue are independent sets. Among other results it is shown that each star set of a connected graph G with three distinct eigenvalues induces a clique if and only if G = K1, 2 or K2, ..., 2. It is also proved that stars are the only graphs with three distinct eigenvalues having a star partition with independent star sets. © 2008 Elsevier Inc. All rights reserved
  5. Keywords:
  6. Galaxy graph ; Star set ; Cobalt ; Cobalt compounds ; Clique ; Co-clique ; Connected graphs ; Eigenvalue ; Eigenvalues ; Graph with three eigenvalues ; Independent sets ; Graph theory
  7. Source: Linear Algebra and Its Applications ; Volume 430, Issue 1 , 2009 , Pages 504-510 ; 00243795 (ISSN)
  8. URL: https://www.sciencedirect.com/science/article/pii/S0024379508003972