Sufficient Conditions for Graphs to Be k-Connected, Maximally Connected, and Super-Connected

Zhen-Mu Hong, Zheng-Jiang Xia, Fuyuan Chen, Lutz Volkmann and M. Irfan Uddin

Complexity, 2021, vol. 2021, 1-11

Abstract: Let G be a connected graph with minimum degree δG and vertex-connectivity κG. The graph G is k-connected if κG≥k, maximally connected if κG=δG, and super-connected if every minimum vertex-cut isolates a vertex of minimum degree. In this paper, we present sufficient conditions for a graph with given minimum degree to be k-connected, maximally connected, or super-connected in terms of the number of edges, the spectral radius of the graph, and its complement, respectively. Analogous results for triangle-free graphs with given minimum degree to be k-connected, maximally connected, or super-connected are also presented.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:5588146

DOI: 10.1155/2021/5588146

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