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arXiv · 2607.25221

Some Spectral Properties of the $B_α$ Matrix of a Graph

Garrett Kepler
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Abstract

Recently, Samanta et al. introduced a unifying perspective to common graph-associated matrices through the matrix $B_α(G)=αA(G)+(1-α)L(G)$ where $α\in [0,1]$. We resolve an open problem regarding the positive semi-definiteness of $B_α$ and similar matrices. We also explore eigenvector properties of $B_α$ through edge and vertex removal. As a consequence, we provide a basis for results on the common graph-associated matrices.

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Garrett Kepler. 2026-07-28. Some Spectral Properties of the $B_α$ Matrix of a Graph. https://arxiv.org/abs/2607.25221

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