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Graphs with integer matching polynomial zeros

Akbari, S ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1016/j.dam.2017.02.009
  3. Abstract:
  4. In this paper, we study graphs whose matching polynomials have only integer zeros. A graph is matching integral if the zeros of its matching polynomial are all integers. We characterize all matching integral traceable graphs. We show that apart from K7∖(E(C3)∪E(C4)) there is no connected k-regular matching integral graph if k≥2. It is also shown that if G is a graph with a perfect matching, then its matching polynomial has a zero in the interval (0,1]. Finally, we describe all claw-free matching integral graphs. © 2017 Elsevier B.V
  5. Keywords:
  6. Graphic methods ; Claw-free ; Integral graphs ; Matching integral ; Matching polynomial ; Perfect matchings ; Polynomials
  7. Source: Discrete Applied Mathematics ; Volume 224 , 2017 , Pages 1-8 ; 0166218X (ISSN)
  8. URL: https://www-sciencedirect-com/science/article/pii/S0166218X1730094X?via%3Dihub