Some Properties Of Integral Circulant Graphs

Integral circulant graph X_n(D) has the vertex set Z_n={0,1,2,..., n1} and vertices a andb are adjacent if and only if gcd(a b, n)∈D, where D is a set of positive, proper divisors ofn. Integral circulant graphs are highly symmetric, and they are widely applied in our life. Inrecent years, more and more experts devoted theirselves to the field, and the integral circulantgraph has become a popular topic. The body of the thesis is divided into four chapters:In Chapter1of this paper, we summarize the history of integral circulant graphs, the back-ground and main results of this paper. In addition, we give the basic concepts of graph theorywhich will be used in the next chapters.In Chapter2, we obtain a new characterization of integral circulant graph, and prove thatall the integral circulant graphs are vertex-transitive and regular. We also determine the edge-connectivity of the integral circulant graphs, and prove that when the unitary Cayley graph isstrongly regular. In addition, we determine that some integral circulant graphs are completegraphs or complete k-partite graphs, and we evaluate the size of the automorphism group ofsome integral circulant graphs.In Chapter3, we research the planarity and independence number of some integral circulantgraphs, and completely evaluate the size of the maximum matching of integral circulant graphs.In Chapter4, we evaluate the diameter and edge chromatic number of the integral circulantgraph X_n(1, d), and determine the perfectness of some integral circulant graphs.