具有多个强正则自补图的最小阶数

The Smallest Older with more Strongly Regular Self-complementary Graphs

本文应用两个不同构的13阶强正则自补图,解决了Kotzig在1979年提出尚未解决的问题:“至少存在两个非同构的4k+1个顶点的强正则自补图集中,其最小整数k是什么?”,获得了最小整数k=3,并且否定了Kotzig在这个问题上所获得的结果.

In this paper, by using two nonisomorphic strongly regular self-complementary graphs with 13 vertices, the author solves the unsolved problem presented by Kotzig in 1979:'What is the smallest integer k with the property that there exist at least two nonisomorphic strongly regular self-complementary graphs on 4k+1 vertices?', and proves that the smallest integer k is 3, and also negatives the result obtained by Kotzig.