On the A-spectral radius of graphs with given size and diameter

Feng, Zhimin; Wei, Wei

doi:10.1016/j.laa.2022.06.006

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Cited by 10 publications

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“…Lin, Huang and Xue [16] characterized the graph with the maximum α-index among all connected graphs with order n and cut vertices k. Guo and Zhang [14] determined the graphs with the maximum α-index for α ∈ [ 1 2 , 1) among the C 4 -free (resp. Halin) graphs with order n. For more results, one can refer to [11,12,18,28,32]. In recent years, the relationship between the spectral parameter and forbidden subgraphs has been a hot research topic.…”

Section: Introductionmentioning

confidence: 99%

On the $α$-index of minimally 2-connected graphs with given order or size

Lou¹,

Wang²,

Yuan³

2023

Preprint

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For any real α ∈ [0, 1], Nikiforov defined the A α -matrix of a graph G as, where A(G) and D(G) are the adjacency matrix and the diagonal matrix of vertex degrees of G, respectively. The largest eigenvalue of A α (G) is called the α-index or the A α -spectral radius of G. A graph is minimally k-connected if it is k-connected and deleting any arbitrary chosen edge always leaves a graph which is not k-connected. In this paper, we characterize the extremal graphs with the maximum α-index for α ∈ [ 1 2 , 1) among all minimally 2-connected graphs with given order or size, respectively.

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