Research On Two Classes Domination Number Of Circulant Graphs

Domination in graphs is one of the most active fields in graph theory,and domination number of graphs is one of the important problems.Caculating the domination number or determining a better domination number bound of any graph is difficult and complicated.Especially for a certain type of graph,it is very difficult to give a uniform and good domination number.Circulant graphs are a classical graph in graph theory.The vertices and edges of a circulant graph have good rotation symmetry,thus the circulant graph is a research object in many graph theory problems.In this paper,two classes domination numbers of circulant graph are studied,including the total signed domination number and the Italian domination number.In this paper,the lower bounds of the total signed domination number and the Italian domination number are obtained by combining the total signed domination number and the Italian domination number of general graphs with the properties of circulant graph.In this paper,when we study the two classes domination number upper bounds of circulant graph,we first use the computer to find the two classes domination number of the smaller-scale circulant graph and construct the corresponding dominating functions,then introduced the two classes domination number of the larger circulant graph and verified by the computer,finally gave a better conclusion,including some accurate value.