Distance matrix of a multi-block graph: determinant and inverse

被引：5

作者：

Das, Joyentanuj ^{[1
]}

Mohanty, Sumit ^{[1
]}

机构：

[1] IISER Thiruvananthapuram, Sch Math, Maruthamala PO, Thiruvananthapuram 695551, Kerala, India

来源：

LINEAR & MULTILINEAR ALGEBRA | 2022年 / 70卷 / 19期

关键词：

m-partite graphs; Laplacian-like matrix; distance matrix; determinant; cofactor;

D O I：

10.1080/03081087.2020.1860886

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A connected graph is called a multi-block graph if each of its blocks is a complete multipartite graph. We consider the distance matrix of multi-block graphs with blocks whose distance matrices have nonzero cofactor. In this case, if the distance matrix of a multi-block graph is invertible, we find the inverse as a rank one perturbation of a multiple of a Laplacian-like matrix. We also provide the inverse of the distance matrix for a class of multi-block graphs in which the distance matrix of one of its block has zero cofactor.

引用

页码：3994 / 4022

页数：29

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