Toughness and spectral radius in graphs

2023/10/14 by Chen, Yuanyuan, Fan, Dandan, Lin, Huiqiu · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.09523

Abstract

The Brouwer's toughness conjecture states that every d-regular connected graph always has t(G)>\fracdλ-1 where λ is the second largest absolute eigenvalue of the adjacency matrix. In 1988, Enomoto introduced a variation of toughness τ(G) of a graph G. By incorporating the variation of toughness and spectral conditions, we provide spectral conditions for a graph to be τ-tough (τ≥ 2 is an integer) and to be τ-tough (\frac1τ is a positive integer) with minimum degree δ, respectively. Additionally, we also investigate a analogous problem concerning balanced bipartite graphs.

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• Sufficient conditions for even factors in graphs
• Scattering number and τ-toughness in graphs involving A_α-spectral radius

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