摘要
Let G be any non-abelian group and be its center. The non-commuting graph of G is the simple graph whose vertex set is , with two vertices x and y adjacent whenever . We prove that if is isomorphic to the non-commuting graph of the alternating group (), then . This result together with a recent one due to Solomon and Woldar gives a complete positive answer to a conjecture proposed in [A. Abdollahi, S. Akbari, H.R. Maimani, Non-commuting graph of a group, J. Algebra 298 (2006) 468-492]: If S is any finite non-abelian simple group such that for some group G, then .