Non-Singular Trees, Unicyclic Graphs and Bicyclic Graphs

• 作者: Chengling Xie Danyang Li Haicheng Ma
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: ADJACENCY MATRIX Non-Singular RANK NULLITY
• 年，卷（期）: 2020,（1）
• 页码范围: 1-7
• 页数: 7页
• 分类号: O15

摘要

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) or?θ(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.