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Bibliographic Details
Main Authors:	Pastén, Germain, Oliveira, Carla Silva, Junior, João Domingos G. da Silva, Justel, Claudia M.
Format:	Preprint
Published:	2025
Subjects:	Discrete Mathematics 05C50, 05C05
Online Access:	https://arxiv.org/abs/2510.16812
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Table of Contents:

Let $G$ be a graph with adjacency matrix $A(G)$ and Laplacian matrix $L(G)$. In 2024, Samanta \textit{et} \textit{al.} defined the convex linear combination of $A(G)$ and $L(G)$ as $B_α(G) = αA(G) + (1-α)L(G)$, for $α\in [0,1]$. This paper presents some results on the eigenvalues of $B_α(G)$ and their multiplicity when some sets of vertices satisfy certain conditions. Moreover, the positive semidefiniteness problem of $B_α(G)$ is studied.