On edge-path eigenvalues of graphs

Akbari, S ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1080/03081087.2020.1820934
  3. Publisher: Taylor and Francis Ltd , 2020
  4. Abstract:
  5. Let G be a graph with vertex set (Formula presented.) and (Formula presented.) be an (Formula presented.) matrix whose (Formula presented.) -entry is the maximum number of internally edge-disjoint paths between (Formula presented.) and (Formula presented.), if (Formula presented.), and zero otherwise. Also, define (Formula presented.), where D is a diagonal matrix whose i-th diagonal element is the number of edge-disjoint cycles containing (Formula presented.), whose (Formula presented.) is a multiple of J−I. Among other results, we determine the spectrum and the energy of the matrix (Formula presented.) for an arbitrary bicyclic graph G. © 2020 Informa UK Limited, trading as Taylor & Francis Group
  6. Keywords:
  7. Edge-connectivity ; Edge-path energy ; Eigenvalue
  8. Source: Linear and Multilinear Algebra ; 2020
  9. URL: https://www.tandfonline.com/doi/abs/10.1080/03081087.2020.1820934?journalCode=glma20