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arXiv · 2301.02733

Bounds for a alpha-eigenvalues

João Domingos G. da Silva Jr·Carla Silva Oliveira·Liliana Manuela G. C. da Costa
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Abstract

Let G be a graph with adjacency matrix A(G) and degree diagonal matrix D(G). In 2017, Nikiforov [1] defined the matrix Aalpha(G), as a convex combination of A(G) and D(G), the following way, Aalpha(G) = alpha A(G) + (1 - alpha)D(G), where alpha belongs to [0,1]. In this paper, we present some new upper and lower bounds for the largest, second largest, and smallest eigenvalue of the Aalpha-matrix. Moreover, extremal graphs attaining some of these bounds are characterized

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João Domingos G. da Silva Jr, Carla Silva Oliveira, Liliana Manuela G. C. da Costa. 2023-01-06. Bounds for a alpha-eigenvalues. https://arxiv.org/abs/2301.02733

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