S图的若干必要条件

Some Necessary Conditions for Constructing S-graph

满足Ｇ２≌Ｇ的图Ｇ称为Ｓ图．本文的主要结果为：若Ｇ是Ｓ图，则ｄｉａｍ（Ｇ）＝３或４（其中ｄｉａｍ（Ｇ）表示图Ｇ的直径），并且ｒ（Ｇ）＞２（ｒ（Ｇ）表示图Ｇ的半径），△（Ｇ）≤ｐ—５（△（Ｃ）表示图Ｇ的顶点的最大度数，ｐ表示图Ｇ的顶点的个数）；若Ｇ是Ｓ图，则ｐ≥７，ｐ≤７的图只有Ｇ７是Ｓ图；△（Ｇ）＝２的图只有Ｇ７是Ｓ图．

Graph G is called S-graph if G2≌G. The main conclusion in this poper is as follows:Let G be S-graph, then its diameter diam (G )=3 or 4 and its radius r(G)>2, moreover,△(G )≤p-5 and p≥7, where p and △ (G ) denote the number and maximum degree of venices of G. Particularly,when p≤7 or △ (G ) =2, only C7 is S-graph.