Article ID Journal Published Year Pages File Type
4603375 Linear Algebra and its Applications 2008 11 Pages PDF
Abstract

The minimum rank of a graph G is defined as the smallest possible rank over all symmetric matrices governed by G. It is well known that the minimum rank of a connected graph is at least the diameter of that graph. In this paper, we investigate the graphs for which equality holds between minimum rank and diameter, and completely describe the acyclic and unicyclic graphs for which this equality holds.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory