17阶强正则自补图的唯一性

THE UNIQUE OF STRONGLY REGULAR SELF-COMPLAMANTARY GRAPH WITH ORDER 17

本文不使用“块次矩阵”的方法,获得一个强正则图是17阶强正则自补图的充要条件:1)p=17,k=8,λ=3,=4;2)对于u∈V(G),u的邻点导出子图为8阶3度正则图,且u的不邻点导出子图为8阶4度的正则图.由此证明17阶强正则自补图是唯一的,从而将文献[2]中的结论k≥4改进为k≥6.

In this paper, we need not ＂block -degree matrix＂ method, but obtain a necessary and sufficient conditions of strongly regular self - eomplamantary graphs： 1 ）p = 17 ,k = 8,A = 3 ,μ= 4 ; 2）. The induced subgraph of neighbourhood about any vertex is a graph of 3 - degree regular with order 8 ; and the induced subgraph of non -neighbourhood about any vertex is a graph of 4 - degree regular with order 8. Then the author applies this condition to proof that the strongly regular self - complamantary graph is unique. Thereby the conclusion in the reference[2] is improved to that it is k≥6.