一个伴随等价定理的推广及其简证

Short Proof and Popularization of a Adjoint Equivalence Theorem

记 Gr为任意图 G的 r个拷贝中的对应点 ( r个 )分别与星图 Sr+ 1 的 r个 1度点粘接后得到的图 ,又记 H r为该图 G的相应点与星图 Sr+ 1 的 r度点粘接后得到的图 .如果 G不含三角形 ,则图 ( r- 1) K1 ∪ Gr和图 ( r- 1) G∪ H r伴随等价 。

Let Gr be the graph consisting of star graph S r+1 and the r′s copies of any graph G by coincidin g a same vertex of G with a vertex of degree 1 of star graph S r+1 ,and Let Hr be the graph consisting of star graph S r+1 and a ny graph G by coinciding a vertex of G with the vertex of degree r of S r+1 , if G not contain triangle, then Gr∪(r-1)K 1 and (r-1)G∪Hr adjoint equivalent. Hence its complement graph that be chroma tic equivalent.