Research On Magic And Anti-Magic Algorithms Of Random Graphs

Graph theory is an important part of computer and combinatorial mathematics.It takes graph as the object of study and has important research value in computer theory,operations research and machine learning.At present,the development of the computer has become a significant driving force promoting the development of various disciplines,thus,the appearance of the computer has greatly promoted the development of graph theory.Graph labeling,originated from the elegant conjecture put forward by Rosa,is an important branch of graph theory with a wide range of use value.Many problems in real life can be abstracted into the problems of graph labeling,which can be solved by theoretical analysis of graph labeling.There are various graph labeling,among which there are graceful labeling,magic labeling and felicitous labeling.In magic labeling,there exist many studies on the edge total labeling and the total labeling,but the traditional research methods mostly adopt the combinatorial construction method,which can only prove the graphs with rules and certain structures.Due to the limitations of the combination of the traditional construction method,it' s hard to give a random graph related conclusions.In order to make the comprehensive study of edge magic graph,with the aid of the high computing power of computer and the methods optimizing labeling solution space of the traditional measures,adopting the approach of recursive backtracking,the edge total labeling algorithm is designed in this paper.Verifying all the edge total labeling of simple connected graphs within 9 points,and the related conclusions of them are obtained.As the number of connected graphs increases exponentially with the number of points and edges,and because the solution space is relatively large,all trees within 17 points,all unicyclic graphs within 16 points and all bicyclic graphs within 15 points are selected for the verification of edge totaling labeling.Analyzing of the experimental results,the relevant theorems in finite points are obtained and the corresponding conjectures are put forward.Based on these conjectures,the graphs with large points are verified to judge whether the guesses are valid or not.By modifying the total labeling algorithm,total label algorithm with all solutions and the total labeling fuzzy matching algorithm are obtained.By using these three algorithms and combining with the regular expression,this paper discusses the present problems about edge total labeling,proving,checking some of them and giving some ideas of proof.The computer can only get limited point random graphs instead of a family of graphs,using composite construction method and making full use of computer,defining a few class of join-graphs.With magic the edge-magic total labeling algorithm,getting all the solutions of graphs within finite points,and by composite construction method,giving he mathematical proof of these kinds of join-graphs,which gives full play to the advantages of computers and combinatorial construction.According to the connection between edge-magic total labeling and(a,d)-edge-antimagic total labeling and the experience of designing edge-magic total labeling algorithms,the algorithm for(a,d)-edge-magic total labeling is designed.Because the solution space of(a,1)-edge-antimagic total labeling is too large,the verification are carried out for all tree graphs within 11 points,and so are the(a,d)-edge-antimagic total labeling where d=1,d=2 and d=3 for all graphs within 6 points.According to the labeling results of graphs within the finite points,the(a,d)-edge-antimagic total labeling of some special graphs under different d conditions are proved.