直径为偶数的A(H)=3图的存在问题

Existence Problem of Even Diameter Graphs with A(H)=3

针对目前所构造的A(H)=3图的共同特点是图的直径都是奇数,是否存在直径为偶数的A(H)=3图问题,利用A(H)=2图母图的性质,通过讨论特殊点的联系数,构作了直径为偶数的A(H)=3图的一个无限图类,说明偶直径的3—图是存在的,且是不惟一的,从而解决了偶直径的3—图的存在惟一性问题。

The common feature of constructed graphs with A(H)=3 is: the diameters are all odd. Are there any possibilities that even diameter graphs with A(H)=3 exist? In the light of this problem, this paper makes use of the original graph's quality with A(H)=2, calculates the special spots' eccentricity and constructs and infinite class of graphs with A(H)=3, thereby we illustrate these graphs are existent but ununique, so to solve the unique problem of the existence of even diameter graphs with A(H)=3.