The Supereulerianity Of Two Classes Of Digraphs Operations

With the development of science and technology,the rise of all walks of life,the re-quirement of the basic subject of mathematics is higher and higher,the graph theory in discrete mathematics is more and more popular among scholars,the interest in graph theory undoubtedly contributed to its development,it is not only the theoretical research that has been improved,but also the application of it in life.Graph theory is a new branch of math-ematics that has developed rapidly in the past 210 years.Late 19th century,graph theory has been used to study the system of electrical network and molecular structure in organic chemistry.Soon after,with the rise of computer technology,graph theory was no longer confined to its own development,combined with computer technology,it can not only solve many problems in graph theory but also apply to all walks of life,success combines theory with practice.Because of this,the development of graph theory has attracted the attention of many researchers.The content of graph theory is very rich,involve a wide range.This paper is only concerned with the supereulerian problem in graph theory,the supereulerianity of the digraph is an important and novel research direction of graph theory.Therefore,The supereulerianity of the digraph has become a hot research in graph theoryThrough discussion,we learned some classes of digraphs.For example,strong product,pth power,are digraphs obtained by some simple digraphs with special operation.The research about the supereulerianity is an innovative breakthrough.Both the theorem and the proof process are novel straightforward.This paper mainly studies the supereulerianity of some special classes of digraphsThe text of the paper consists of three chapters:In the first chapter,firstly,we introduce the research background and status quo and basic concepts needed of supereulerian digraph,then,give definitions of strong product,pth power,etc.Finally,we introduce contents and main result in this paper.In the second chapter,according to the definition of strong product digraph,we obtain the property of strong product digraphs and the relationship of vertex,arc and degree;sec-ondly,we obtain the supereulerianity of the strong product digraph of D1 and D2,and by giving the inverse example,the result is optimal;finally,we obtain the sufficient conditions on the strong product digraph of D1 and D2 to be bi-trailable digraph.In the third chapter,we first show the background of pth power.Finally,we mainly research the sufficient conditions on the pth power of digraphs to be supereulerian digraph,and by giving the inverse example,the result is optimal.