Some resistance distance and distance-based graph invariants and number of spanning trees in the tensor product of P2 and Kn

Abstract

The resistance distance (Kirchhoff index and multiplicative Kirchhoff index) and distance-based (Wiener index and Gutman index) graph invariants of Γn = P2 ×Kn are considered. Firstly by using the decomposition theorem, we procure the Laplacian and Normalized Laplacian spectrum for graph Γn, respectively. Based on which, we can procured the formulae for the number of spanning trees and some resistance distance and distance-based graph invariants of graph Γn. Also, it is very interesting to see that when n tends to infinity, Kf (Γn) is a polynomial and W (Γn) is a quadratic polynomial.