Research On Reducible Coloring Algorithm Of Random Graph With Distance β

Graph theory originated from the Konigsberg seven bridge problem and is closely related to mathematics.At present,it has very important research and application in the field of computer and mathematics.Graph coloring is a research point of graph theory,which is also widely used,especially for solving combinatorial optimization problems.Many problems in reality can be abstracted into random graphs and then solved by graph coloring methods,such as map coloring,task scheduling,maximum dominance,matrix operation,communication coding and decoding and so on.It can be seen from the published literature that the existing coloring methods and results can only solve the practical problem of abstracting into special graphs or some random graphs with less points.There is no better research method for random graphs with larger points,which has certain limitations.Therefore,it has become a new trend to design algorithms and apply computer technology to solve the graph coloring problem of large number of random graphs.This paper aims to use computer to design relevant algorithms to study and analyze random graphs in finite points,and try to solve the problem that the distance of random graphs in finite points is β And try to prove the existing guesses by using the algorithm combined with the program results,hoping to apply the research of reducible coloring to more fields.In this paper,the D(β)reducible edge coloring problem of random graphs is studied,and the research and analysis are carried out from the perspectives of color sum and color set,respectively,and a research scheme to solve such problems is proposed,and new adjacent vertex sum reducible edges are designed.Coloring algorithm,D(2)-vertex sum reducible edge coloring algorithm,D(β)-vertex reducible edge coloring algorithm.The iterative optimization method is used to solve all non-isomorphic graphs within a finite point,and these algorithms are used to classify the obtained data set,and obtain all non-isomorphic graphs within 10 points and all special graphs within 15 points.The coloring matrix and the maximum coloring number,and summarize the experimental results,analyze the statistical results to obtain the coloring conclusion of adjacent vertex sum reducible edges of several graphs,D(2)-vertex sum reducible edge coloring conclusions,and adjacent vertex reducible edges coloring conclusion,D(2)-vertex reducible edge coloring conclusion.The specific coloring results and theorem proofs of some simple graphs and special graphs and their associated graphs are also given.In view of the large number of random map atlases with more than 10 points,only some atlases are selected for research to verify the possibility of guessing.