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

Authors

R. Balaji, Indian Institute of Technology Madras
R. B. Bapat, Indian Statistical Institute (Delhi Centre)
Shivani Goel, Indian Institute of Technology Madras

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

Comments

Open Access, Green

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