arXiv subjects

Liliana Manuela G. C. da Costa

Publications and source records attributed to Liliana Manuela G. C. da Costa.

2 recordsLinked to original sources

arXiv2023

Bounds for a alpha-eigenvalues

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

cs.DM↗

arXiv2022

On the characteristic polynomial of the $A_α$-matrix for some operations of graphs

Let G be a graph of order $n$ with adjacency matrix $A(G)$ and diagonal matrix of degree $D(G)$. For every $α\in [0,1]$, Nikiforov \cite{VN17} defined the matrix $A_α(G) = αD(G) + (1-α)A(G)$. In this paper we present the $A_α(G)$-characteristic polynomial when $G$ is obtained by coalescing two graphs, and if $G$ is a semi-regular bipartite graph we obtain the $A_α$-characteristic polynomial of the line graph associated to $G$. Moreover, if $G$ is a regular graph we exhibit the $A_α$-characteristic polynomial for the graphs obtained from some operations.

cs.DM↗