Loading...

An inequality using perfect matchings and laplacian spread of a graph

Akbari, S ; Sharif University of Technology | 2019

298 Viewed
  1. Type of Document: Article
  2. DOI: 10.1080/03081087.2017.1418823
  3. Publisher: Taylor and Francis Ltd , 2019
  4. Abstract:
  5. Let G be a simple connected graph of order n. Let (Formula presented.) be the Laplacian eigenvalues of G. In this paper, we show that if X and Y are two subsets of vertices of G such that (Formula presented.) and the set of all edges between X and Y decomposed into r disjoint perfect matchings, then, (Formula presented.) where (Formula presented.). Also, we determine a relation between the Laplacian eigenvalues and matchings in a bipartite graph by showing that if (Formula presented.) is a bipartite graph, (Formula presented.) and (Formula presented.), then G has a matching that saturates U. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group
  6. Keywords:
  7. 05C50 ; 15A18 ; Laplacian matrix ; Matchings ; Spread
  8. Source: Linear and Multilinear Algebra ; Volume 67, Issue 3 , 2019 , Pages 442-447 ; 03081087 (ISSN)
  9. URL: https://www.tandfonline.com/doi/abs/10.1080/03081087.2017.1418823?journalCode=glma20