完全二部图的邻接谱(英文)

Adjacent spectral characterization of complete bipartite graphs

给出了完全二部图邻接谱的刻画:若m,n是两个正整数,则完全二部图K_(m,n)由它的邻接谱决定当且仅当m,n是素数,或n是素数且m的每个真因子不大于n,或m,n是合数且使得对任意的满足m′n′=mn的m′,n′,m′+n′≥m+n.

The adjacent spectral characterization of complete bipartite graphs was given in this paper： Let m, n be two positive integers. Then the complete bipartite graphs Km, n are determined by their adjacency spectrum if and only if any one of the following conditions holds： m, n are prime; n is a prime and every proper divisor of m not greater than n; m, n are composite numbers such that m＇ ＋ n＇≥ m ＋ n for any integers rn＇ and n＇ with m＇n＇= ran.