Spanning Trees of Bounded Degree, Connectivity, Toughness, and the Spectrum of a Graph

Cunxiang Duan, Ligong Wang

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Recently, Cioabǎ and Gu obtained a relationship between the spectrum of a regular graph and the existence of spanning trees of bounded degree, generalized connectivity and toughness, respectively. In this paper, motivated by the idea of Cioabǎ and Gu, we determine a connection between the (signless Laplacian and Laplacian) eigenvalues of a graph and its structural properties involving the existence of spanning trees with bounded degrees and generalized connectivity, respectively. We also present a connection between the (signless Laplacian and Laplacian) eigenvalues and toughness of a bipartite graph, respectively. Finally, we obtain a lower bound of toughness in a graph in terms of edge connectivity κ and maximum degree Δ.

Original languageEnglish
Pages (from-to)185-196
Number of pages12
JournalBulletin of the Iranian Mathematical Society
Volume47
Issue number1
DOIs
StatePublished - Feb 2021

Keywords

  • Connectivity
  • Eigenvalue
  • Spanning k-tree
  • Toughness

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