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arXiv · 2501.03806

Bounds on $A_\alpha$-eigenvalues using graph invariants

João Domingos Gomes da Silva Junior·Carla Silva Oliveira·Liliana Manuela Gaspar Cerveira da Costa
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Abstract

In 2017, Nikiforov introduced the concept of the $A_{\alpha}$-matrix, as a linear convex combination of the adjacency matrix and the degree diagonal matrix of a graph. This matrix has attracted increasing attention in recent years, as it serves as a unifying structure that combines the adjacency matrix and the signless Laplacian matrix. In this paper, we present some bounds for the largest and smallest eigenvalue of $A_{\alpha}$-matrix involving invariants associated to graphs.

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João Domingos Gomes da Silva Junior, Carla Silva Oliveira, Liliana Manuela Gaspar Cerveira da Costa. 2025-01-07. Bounds on $A_\alpha$-eigenvalues using graph invariants. https://arxiv.org/abs/2501.03806

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