Brown, M., Kennedy, J.W. and Servatius, B. (1993) Graph Singularity. Graph Theory Notes of New York, 25, 23-32.

has been cited by the following article:

• TITLE: Non-Singular Trees, Unicyclic Graphs and Bicyclic Graphs

  AUTHORS: Haicheng Ma, Danyang Li, Chengling Xie

  KEYWORDS: Adjacency Matrix, Non-Singular, Rank, Nullity

  JOURNAL NAME: Applied Mathematics, Vol.11 No.1, December 31, 2019

  ABSTRACT: We called graph G non-singular if adjacency matrix A (G) of G is non-singular. A connected graph with n vertices and n-1, n and n+1 edges are called the tree, the unicyclic graph and the bicyclic graph. Respectively, as we all know, each connected bicyclic graph must contain ∞(a,s,b) orθ(p,l,q) as the induced subgraph. In this paper, by using three graph transformations which do not change the singularity of the graph, the non-singular trees, unicyclic graphs and bicyclic graphs are obtained.