Supereulerianity Of L-path Sum Of Two Graphs And Small Graphs

In this dissertation,we systematically study some problems about the supereulerian-ity of graphs,including supereulerian(di)graphs on l-path sum of two(di)graphs,l-path sum of two(di)graphs,which are symmetrically connected or partially symmetric,and the supereulerianity of small graphs.The whole thesis is divided into three chapters.In Chapter 1,a survey to the background and history is presented for supereulerianity of graphs,including Catlin’s reduction method and some related results.The related conclu-sions about the supereulerian graphs on the 2-sum of two digraphs,and small supereulerian graphs are presented.At the end of this chapter,we will introduce some notations and terminologies.Chapter 2,based on the 2-sum of two digraphs investigated by Alsatami et al.,we present the l-path sum of two(di)graphs as an extention of 2-sum,and study sufficient conditions for l-path sum to be supereulerian.Moreover,we discuss the l-path sum of two symmetrically connected digraphs or partically symmetric digraphs.Since Catlin’s reduction method was proposed in 1988,many supereulerian graphs and related topics have been boiled down to the investigation of small graphs.In the last chapter,we characterize non-supereulerian 2-edge-connected graphs with no more than 9 vertices.