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ON SOME SPECTRAL PROPERTIES OF GRAPHS IN TERMS OF THEIR MAXIMUM MATCHINGS AND MINIMUM VERTEX COVERS
Keywords:
spectral radius, principal eigenvector, walks, minimum vertex cover number, independence number, clique number.DOI:
https://doi.org/10.17654/0974165822043Abstract
The principal eigenvector of a graph $G$ is the unique non-zero unit vector corresponding to the spectral radius $\lambda_1$ of $G$. In this paper, we present some bounds on the minimal entry $x_{\min }$ as well as on the ratio $\frac{x_{\max }}{x_{\min }}$ of the maximal entry to the minimal entry of the principal eigenvector $X$ of a graph $G$ in terms of the spectral radius $\lambda_1$, 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 $G$.
Received: August 7, 2022
Accepted: September 26, 2022
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