The Application Of The Label Of The Graph In Management

Background:In 2007,the World Radiocommunication Conference opened in Geneva,Switzerland.At the first China Radio Conference,Wang Xinzhe,chief economist of the Ministry of Industry and Information Technology,emphasized that we should manage the spectrum resources well and guide the radio industry to achieve high-quality development.In 2018,the 18th ITU(International Telecommunication Union)World Telecom Exhibition opened in Durban,South Africa.Facing the future 5G business,Vice Minister of Industry and Information Technology Chen Zhaoxiong put forward three proposals in his speech:first,to promote the efficient use of spectrum resources;second,to promote the coordinated development of industry,closely adhere to the international standards of 3GPP5G,strengthen the division of labor and cooperation in the global industrial chain;third,to promote the wide application of technology.Radio spectrum is a limited natural resource.It is widely used in communication and other fields.With the rapid development of computer network technology,the storage,processing and sharing of network information plays an increasingly important role in people’s daily life.The data services carried by public mobile communications are increasing,and the spectrum bandwidth required is increasing.The use of spectrum resources of information is also increasing,and the number of radio stations is increasing rapidly.Therefore,it is inevitable that the frequency is not allocated enough.However,the shortage of frequency limits the development of radio services.However,due to the characteristics of high frequency radio transmission,human beings can not exploit and utilize frequencies above 3000GHz,and the frequency is limited in a certain region,a certain time and a certain condition.Therefore,how to tap the potential of radio spectrum technically and how to manage and use radio frequency scientifically has become a question for spectrum managers to think about.Objective and Significance:Through scientific means,frequency resources are planned and allocated.On the one hand,the regular distribution of radio frequency signals is realized to minimize interference.On the other hand,from the perspective of practical application,the optimal frequency allocation scheme is obtained to meet the needs of frequency utilization.Aiming at the problem of channel resource management,we simulate the distribution of radio stations in reality by mathematical model.We can regard the radio stations in the real world as vertices in the graph,and the limited number of channel signals as L(2,1)-labeling number.Channel signal allocation for radio is equivalent to L(2,1)-labeling number allocation for vertices.Through the analysis of graph model,we need to find out the least L(2,1)-labeling numberIn 1992,Griggs and Yeh[1]transformed the channel assignment problem into a graph labeling problem,and considered the general case of L(2,1)-labeling problem.They conjectured that for any graph G,it satisfies X(G)≤Δ2.At the same time,they proved that for any graph G,it satisfies X(G)≤Δ2+2Δ.Up to now,the conjecture has not been completely solved.Only some special graphs,such as chord graphs,graphs with two diameters,distance graphs and generalized Petersen graphs have been verified.Aiming at the management of channel resource problem,we simulate the distribution of real radio stations by mathematical model.The real radio stations can be regarded as the vertex of the graph,and the limited number of channel signals can be regarded as the L(2,1)-labeling number.Channel signal allocation for radio is equivalent to L(2,1)-labeling number allocation for vertices.Through the analysis of graph model,we need to find the least L(2,1)-labeling number.Since the L(2,1)-labeling number’s restriction of a graph has practical significance,the theoretical results of our study can provide a theoretical basis for the practical management of channel allocation.By applying the theoretical results to the actual distribution of radio stations,we can save the actual use of spectrum resources and optimize the allocation of spectrum resources.Methods:This paper mainly adopts the methods of literature analysis and mathematical model analysis.Through literature analysis,we can understand the research status and research methods at home and abroad,and select a reasonable labelling model.In the mathematical model analysis method,we mainly choose the structural analysis method.This method is to find the inevitable substructures in the graph by studying the structural properties of the graph,and then to summarize and prove these substructures.After completing the theoretical research,we have studied some frequency algorithms,such as exhaustive search algorithm,serial search algorithm,heuristic search algorithm,etc.The research of these algorithms can help us to detect whether the actual frequency resource allocation and theoretical results have good matching,so as to verify the optimization of theoretical results.Results:the theoretical results are improved and the practical problems can be applied to the theory by algorithm.At the same time,the optimization of theoretical results is verified.(1)Theoretical aspect:In 2014,Wang[2]proved that for any Halin graph,the L(2,1)-labeling number of graph G is at most Δ+7;if Δ≥9,the L(2,1)-labeling number of graph G is at mostΔ+2;if Δ=3,the L(2,1)-labeling number of graph G is at most 9.In reference[2],three classical Halin substructures in reference[3]are gived,and three unavoidable substructures are proved by induction.Obviously,three unavoidable substructures are not enough for the pre-improved upper bound of L(2,1)-labeling number of Halin graphs,so we analyze the structure of Halin graphs carefully and find out more unavoidable substructures.For example,when Δ=8,we construct 14 unavoidable substructures,which can also provide research ideas for other coloring problems of Halin graphs.At the same time,we obtain that the L(2,1)-labeling number of graph G is at most Δ+2 when Δ=8.Therefore,we prove that for any Halin graph,the L(2,1)-labeling number of graph G is at most Δ+6.(2)Application aspect:According to the actual needs in life,we can establish the interference network graph between radio stations.When the distance is closer,the interference is stronger.Therefore,we need to allocate a larger difference frequency signal between radio stations.When the distance is closer,the difference of frequency signal can be smaller.This is mainly limited by the distance rule of L(2,1)-labeling number,and then we use the distance rule we established.The labeling algorithm gives the frequency allocation scheme for the interference relation network graph.Combining with the theory,we can get a more optimized frequency allocation scheme.In this way,the actual problem can be solved by the algorithm to achieve the optimal use of spectrum resources.At the same time,the optimization of the theoretical results is verified.