An inverse formula for the distance matrix of a wheel graph with even number of vertices

2020/06/04 by R. Balaji, R.B. Bapat, Balaji, R. +3 · 1 citation
Computer Science · Mathematics · #05C50 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Functional Analysis (math.FA) #Graph Labeling and Dimension Problems #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2006.02841

openalex publication_date 2020/06/04 · openalex created_date 2020/06/12 · openalex updated_date 2026/07/28

Abstract

Let n ≥ 4 be an even integer and W_n be the wheel graph with n vertices. The distance d_ij between any two distinct vertices i and j of W_n is the length of the shortest path connecting i and j. Let D be the n × n symmetric matrix with diagonal entries equal to zero and off-diagonal entries equal to d_ij. In this paper, we find a positive semidefinite matrix \widetildeL such that \rm rank(\widetildeL)=n-1, all row sums of \widetildeL equal to zero and a rank one matrix ww^T such that D^-1=-(1)/(2)\widetildeL + (4)/(n-1)ww^T. An interlacing property between the eigenvalues of D and \widetildeL is also proved.

Cited by

• On generalized inverses of matrices associated with certain graph classes

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