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- W4386651405 abstract "Let G be a connected graph. The toughness of G is defined as t(G)=min{frac{|S|}{c(G-S)}}, in which the minimum is taken over all proper subsets Ssubset V(G) such that c(G-S)geq 2 where c(G-S) denotes the number of components of G-S. Confirming a conjecture of Brouwer, Gu [SIAM J. Discrete Math. 35 (2021) 948--952] proved a tight lower bound on toughness of regular graphs in terms of the second largest absolute eigenvalue. Fan, Lin and Lu [European J. Combin. 110 (2023) 103701] then studied the toughness of simple graphs from the spectral radius perspective. While the toughness is an important concept in graph theory, it is also very interesting to study |S| for which c(G-S)geq l for a given integer lgeq 2. This leads to the concept of the l-connectivity, which is defined to be the minimum number of vertices of G whose removal produces a disconnected graph with at least l components or a graph with fewer than l vertices. Gu [European J. Combin. 92 (2021) 103255] discovered a lower bound on the l-connectivity of regular graphs via the second largest absolute eigenvalue. As a counterpart, we discover the connection between the l-connectivity of simple graphs and the spectral radius. We also study similar problems for digraphs and an edge version." @default.
- W4386651405 created "2023-09-13" @default.
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- W4386651405 date "2023-09-11" @default.
- W4386651405 modified "2023-10-18" @default.
- W4386651405 title "l-connectivity, l-edge-connectivity and spectral radius of graphs" @default.
- W4386651405 doi "https://doi.org/10.48550/arxiv.2309.05247" @default.
- W4386651405 hasPublicationYear "2023" @default.
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