Abstract: The principal eigenvector of a graph G is the unique non-zero unit vector corresponding to the spectral radius λ1 of G. In this paper, we present some bounds on the minimal entry as well as on the ratio of the maximal entry to the minimal entry xmin of the principal eigenvector X of a graph G in terms of the spectral radius λ1, minimum vertex cover number, maximum vertex degree, minimum vertex degree, number of edges and sum of the degrees of vertices contained in a maximum matching of G.
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Keywords and phrases: spectral radius, principal eigenvector, walks, minimum vertex cover number, independence number, clique number.
Received: August 7, 2022; Accepted: September 26, 2022; Published: October 10, 2022
How to cite this article: Bipanchy Buzarbarua and Prohelika Das, On some spectral properties of graphs in terms of their maximum matchings and minimum vertex covers, Advances and Applications in Discrete Mathematics 34 (2022), 57-66. http://dx.doi.org/10.17654/0974165822043
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
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