Explicit formulas for matrices associated to ladder, circular ladder, and Mobius ladder graphs

2023/06/18 by Azimi, Ali, Ghouchan, Mohammad Farrokhi Derakhshandeh
#05C20 #05C50 (Primary) 15A09 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.10497

Abstract

We give explicit formulas for resistance distance matrices and Moore-Penrose inverses of incidence and Laplacian matrices of ladder, circular ladder, and Möbius ladder graphs. As a result, we compute the Kirchhoff index of these graphs and give new combinatorial formulas for the number of their spanning trees.

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