The Super Edge-magic Total Labeling Of Some Classes Of Grapgs And Its Algorithm

This article is aimed at choosing two types of praphs, researching whether they have the algorithm of edge-magic total labeling and super edge-magic total labeling.Let L was a bijective function of simple undirected graph G from V(G)∪E(G)â†'{1,2,…|V(G)∪E(G)|}ï¼› L was said to be a edge-magic total labeling of G and G is a edge-magic total graph if L satisfied the following:for all xy∈E (G), x, y∈V (G) there are the results that L(x)+L(y)+L(xy)=C, C is constant. On the basis of it, if the vertex labeling of G satisfied L(V(G))={1,2,…,|V(G)|}, then L was said to be a super edge-magic total labeling of graph G,G is a super edge-magic total graph.This paper researched the edge-magic total labeling and super edge-magic total labeling of Pn2and Tn,n2, and the corresponding proofs are given with two different algorithm.In Chapter one, we introduce the history of graph theory at first. Secondly, some basic concepts in this article as well as the history background of super edge-magic total labeling. Finally, the problems and progress in the study of this article, as well as some conclusions obtained in this paper.In Chapter two, we give relative conclusions of Pn2and the corresponding proofs are given.In Chapter three, we give relative conclusions of Tn,n2and the corresponding proofs are given.In the fourth chaper, the research of this paper has been summarized, and we also point out some deficiencies in the text. Finally, problems based on this paper has been put forword to be studied fuether.