Some resistance distance and distance-based graph invariants and number of spanning trees in the tensor product of P 2 and K n

摘要

The resistance distance (Kirchhoff index and multiplicative Kirchhoff index) and distance-based (Wiener index and Gutman index) graph invariants of Γ n = P 2 ×K n are considered. Firstly by using the decomposition theorem, we procure the Laplacian and Normalized Laplacian spectrum for graph Γ n , 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 Γ n . Also, it is very interesting to see that when n tends to infinity, Kf (Γ n ) is a polynomial and W (Γ n ) is a quadratic polynomial.