几类基本图的整性

Iitegral Graph In Some Basic Graphs

特征值均为整数的图称为整图。本文研究了几类基本图的整性，证明了圈图C3、C4和C6是整图，Cn（n〉6）是整图的必要条件是n＝8k或n＝16k＋12（k∈n），路图Pn（n＞1）中唯有P2是整图，对n∈N，完全图Kn和完全二部图Kn，n均是整图。

The graph of all eigenvalue are integral number was called integral graph. In this paper studied integral graph in some basic graph, proved cycle graph C3,C4 and C6 are integral graph, the necessary condition of Cn (n > 6) are integral graph is n = 8k or n = 16k + 12(K∈N). In path graph Pn(n >1 ) only P2 is integral graph. For n ∈N, complete graph Kn and complete 2 - partite graph Kn, n are integral graph.