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.

DOI

10.1080/03081087.2020.1840499

Publication Date

1-1-2020

Comments

Open Access, Green

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