On the adjacency matrix of a block graph

被引：16

作者：

Bapat, R. B. ^{[1
]}

Roy, Souvik ^{[2
]}

机构：

[1] Indian Stat Inst, Stat Math Unit, New Delhi 110016, India

[2] Indian Stat Inst, Econ & Planning Unit, New Delhi 110016, India

来源：

LINEAR & MULTILINEAR ALGEBRA | 2014年 / 62卷 / 03期

关键词：

block graph; adjacency matrix; determinant; tree; line graph; 15A15; 05C05; TREES;

D O I：

10.1080/03081087.2013.779268

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A block graph is a graph in which every block is a complete graph. Let G be a block graph and let A be the adjacency matrix of G. We first obtain a formula for the determinant of A over reals. It is shown that A is nonsingular over F2 if and only if the removal of any vertex from G produces a graph with exactly one odd component. A formula for the inverse of A over F2 is obtained, whenever it exists. We obtain some results for the adjacency matrices over F2, of claw-free block graphs, which are the same as the line graphs of trees, and for the adjacency matrices of flowers, which are block graphs with only one cut-vertex.

引用

页码：406 / 418

页数：13

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