复合图G1(u)⊙uv⊙G2(v)的niche数

NICHE NUMBERS OF COMPOSITE GRAPH G 1(u)⊙uv⊙G 2(v)

复合图Ｇ１（ｕ）⊙ｕｖ⊙Ｇ２（ｖ）是将简单图Ｇ１的顶点ｕ与简单图Ｇ２的顶点ｖ用边ｕｖ连接成的图．本文证明：若Ｇ１和Ｇ２都是有限ｎｉｃｈｅ图，则当连接点ｕ，ｖ满足一定的条件时，复合图Ｇ１（ｕ）⊙ｕｖ⊙Ｇ２（ｖ）也是有限ｎｉｃｈｅ图，且ｎ（Ｇ１（ｕ）⊙ｕｖ⊙Ｇ２（ｖ））≤ｎ（Ｇ１）＋ｎ（Ｇ２）－ｒ其中，ｒ＝０，１，２．

The graph G 1(u)⊙uv⊙G 2(v) is the composite graph obtained from linking up the vertex u of simple graph G 1 and the vertex v of simple graph G 2 with a side uv.This paper shows that if both G 1 and G 2 are finite niche graphs and the joints u,v satisfy some conditions,the composite graph G 1(u)⊙uv⊙G 2(v) is indeed a finite niche graph and n(G 1(u)⊙uv⊙G 2(v)≤n(G 1)+n(G 2)-r,and r=0,1,2.