A short note on $A_α$-eigenvalues for simple graphs

Giovanni Barbarino

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arXiv · 2601.18365

A short note on $A_α$-eigenvalues for simple graphs

Giovanni Barbarino

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Abstract

Given a simple graph $G$, its $A_α$ matrix is a convex combination with parameter $α\in [0,1]$ of its adjacency matrix and its degree diagonal matrices. Here we compare two lower bounds presented in [J. D. G. Silva Jr., C. S. Oliveira and L. M. G. C. Costa. "Some results involving the $A_α$-eigenvalues for graphs and line graphs"] for the spectral radius of $A_α$, and prove that one is better than the other when there are no isolated nodes in $G$.

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Giovanni Barbarino. 2026-01-26. A short note on $A_α$-eigenvalues for simple graphs. https://arxiv.org/abs/2601.18365

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