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

08/22/2022

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by   João Domingos G. da Silva Jr., et al.

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Let G be a graph of order n with adjacency matrix A(G) and diagonal matrix of degree D(G). For every α∈ [0,1], Nikiforov <cit.> defined the matrix A_α(G) = α D(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.