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arXiv · 2208.10557

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

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 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.

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João Domingos G. da Silva Jr., Carla Silva Oliveira, Liliana Manuela G. C. da Costa. 2022-08-22. On the characteristic polynomial of the $A_α$-matrix for some operations of graphs. https://arxiv.org/abs/2208.10557

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