Grpah Based Distance Labeling Algorithm And Its Application In Frequency Assignment

Graph theory is a branch of mathematics,especially an important branch of discrete mathematics.In recent decades,graph theory has transformed the problems existing in many fields such as computer flow chart、power grid analysis、artificial intelligence、information search into graph theory problems to solve,and has been widely used to solve the problems of frequency allocation,examination room seating,logistics,timetable and so on,resulting in the rapid development of the research of graph theory.As an important research point in the field of graph theory,icon number problem originated from Rosa’s famous graceful tree conjecture in 1966.Due to different mapping requirements,there are a variety of icon number problems.Among them,the icon numbers concerned by scholars mainly include beautiful label、edge fantasy and full label、L(J,K)– label、 happiness label and so on.At present,in the previous literature on labeling,most of them use the traditional manual reasoning method to label graphs,and this method can only explore the special graph structure,and it is difficult to study the random graphs whose topological structure can not be described by parameters.Researchers’ research on icon numbers mainly focuses on special graph categories,such as fan graph,wheel graph,tree graph,necklace graph,sun graph,bipartite graph and so on.These special graph categories are difficult to reflect the complex problems existing in reality.This paper designs the algorithm for the minimum number of random edges of the graph,and obtains the results of the algorithm for the minimum number of random edges of the graph within 12205208.When the number of random graphs is greater than 11,the number of atlas is very large,which is difficult to label in a short time.Therefore,this paper selects some result sets for research and verifies the correctness of the result set.The L(2,1)– full label of a graph is a kind of icon number,which means that for graph G,if the label values of any two adjacent edges are different,the label numbers of any two adjacent points are different,and the label values of the associated points and edges are different by at least 2,the goal is to obtain the minimum label number of graph G.Based on the analysis of the existing research results of L(2,1)-full labeling of graphs,a full labeling search algorithm is designed,the labeling result sets of 12205208 random graphs within 11 points are obtained,and some labeling conclusions of associative graphs are obtained.The frequency planning problem is essentially a combinatorial optimization problem,assigning a limited number of channels to a larger number of carrier frequencies.Since the number of carrier frequencies is much larger than the number of channels,interference inevitably occurs between different carrier frequencies allocated to the same channel or adjacent channels.In recent years,many scholars have transformed the channel allocation problem into the icon symbol model for research.According to the research results of this paper,the simulation experiment of frequency allocation is obtained through analysis,and a specific allocation scheme is given.The experiment proves the correctness of the algorithm and the practical research value of icon number theory.