Tutte多项式和Akiyama-Harary问题的一个强版本
Tutte polynomials and a stronger version of the Akiyama-Harary problem
摘要：
一个非自补图能有与其补图相同的色多项式吗？秋山和哈拉里的这个问题得到了肯定的回答。刘某他们证明了每一个这样的图都有与它的补图相同的度序列。在本文中，我们表明，有无限多的图，这一猜想不成立。然后，我们解决了一个更一般的变种的秋山-Harary问题表明，存在无限多的非自补图具有相同的Tutte多项式作为其补充。
英文摘要：
Can a non self-complementary graph have the same chromatic polynomial as its complement? The answer to this question of Akiyama and Harrary is positive and was given by J. Xu and Z. Liu. They conjectured that every such graph has the same degree sequence as its complement. In this paper we show that there are infinitely many graphs for which this conjecture does not hold. We then solve a more general variant of the Akiyama-Harary problem by showing that there exists infinitely many non self-complementary graphs having the same Tutte polynomial as their complements.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
