度补图的直径

The Diameter of Degree-Complementary Graph

本文的第一部分对度补图的直径作研究,得出其直径D(G)≤4,并构造出一个直径为4的度补图来说明这一结果不能再改进。第二部分通过对图与其补图的直径分析,从而指明了若D(G)=3,则D(G)=2或3。作者对满足D(G)=3,且D(G)=3的这一类图作了更进一步的分析,得出了其结构性质、构造方法及其全部极图。

The frist part of this paper makes a research to the diameter of degree -complementary graph, results in its diameter D (G) <4, and design the degree -complementary graph (of the D=4) to show that this result can't be improved further. The second part shows that if D (G) is 3, D (G) is 2 or 3 by analyzing the graph and its complement. The auther analyzes more further such the graph that is suitable to D (G) = D (G) =3, and gains its constuction, designing method, and the whole extremal graph.