# On distance matrices of wheel graphs with an odd number of vertices

## Article Type

Research Article

## Publication Title

Linear and Multilinear Algebra

## Abstract

Let (Formula presented.) denote the wheel graph having n-vertices. If i and j are any two vertices of (Formula presented.), define (Formula presented.) Let D be the (Formula presented.) matrix with (Formula presented.) entry equal to (Formula presented.). The matrix D is called the distance matrix of (Formula presented.). Suppose (Formula presented.) is an odd integer. In this paper, we deduce a formula to compute the Moore-Penrose inverse of D. More precisely, we obtain an (Formula presented.) matrix (Formula presented.) and a rank one matrix (Formula presented.) such that (Formula presented.) Here, (Formula presented.) is positive semidefinite, (Formula presented.) and all row sums are equal to zero.

## First Page

3370

## Last Page

3401

## DOI

10.1080/03081087.2020.1840499

## Publication Date

1-1-2022

## Recommended Citation

Balaji, R.; Bapat, R. B.; and Goel, Shivani, "On distance matrices of wheel graphs with an odd number of vertices" (2022). *Journal Articles*. 3432.

https://digitalcommons.isical.ac.in/journal-articles/3432

## Comments

Open Access, Green