Singularity Of Oriented Graphs From Several Classes

Algebraic graph theory is an important branch of discrete mathematics,and the singularity of graph is a hot issue in algebraic graph theory.On this basis,we consider some special oriented graphs and get some new results.A directional graph is a special kind of directed graph in which each edge has one and only one direction.In this paper,the algebraic properties of graphs are used to deal with the singularity of directional graphs.The singularity of directional trees,directional unicyclic graphs,directional biyclic graphs and directional tricyclic graphs are described.The specific research contents are as follows:Chapter 1:We introduce the research background and significance,the research trends at home and abroad and the main structure of this paper.Chapter 2:We introduce the basic knowledge such as the concept and lemma used in the paper.Chapter 3:we describe the singularity of the following three types of graphs:(1)The oriented graphs in which cycles are vertex disjoint;(2)The graphs in which all cycles share exactly one common vertex;(3)the graphs formed by cycles sharing a common path.Then the singularity of directional tree,directional unicyclic graph and directional biyclic graph is derived.Chapter 4:According to the structural characteristics of directional tricyclic graphs,four kinds of directional tricyclic graphs are processed respectively,and then the singularity of directional tricyclic graphs is described.The fifth chapter summarizes the main content of this paper,and put forward the shortcomings of this paper and the future research direction.