Abstract
Let Rsk(G) be the graph obtained from a graph G by gluing k distinct path graphs Ps+2 to both vertices incident to each edge of G. In this paper, we derive a factorization formula for the generalized characteristic polynomial of the graph Rsk(G), where G is regular. As particular cases, we obtain formulas for the characteristic polynomials of the adjacency, Laplacian, normalized Laplacian, and signless Laplacian matrices of Rsk(G), as well as for the Ihara zeta function of Rsk(G), where G is regular. We also derive formulas for the Kirchhoff, additive degree-Kirchhoff, and multiplicative degree-Kirchhoff indices of Rsk(G), where G is regular. In addition, we determine the weighted Kirchhoff index of Rsk(G), for an arbitrary graph G. This work generalizes recent results on semitotal point graphs.
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