The Q-index and connectivity of graphs

2021/09/16 by Pengli Zhang, Zhang, Peng-Li, Feng, Lihua +2
Computer Science · Mathematics · Physics and Astronomy · #05C50 #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #Graph theory and applications #Interconnection Networks and Systems

paper · pdf · doi:10.48550/arxiv.2109.07656

openalex publication_date 2021/09/16 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

A connected graph G is said to be k-connected if it has more than k vertices and remains connected whenever fewer than k vertices are deleted. In this paper, for a connected graph G with sufficiently large order, we present a tight sufficient condition for G with fixed minimum degree to be k-connected based on the Q-index. Our result can be viewed as a spectral counterpart of the corresponding Dirac type condition.

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