图的广义字典序积的强不可缩回性

Strong unretractive property of generalized lexicographic product of graphs

通过对图的广义字典序积的强不可缩回性的讨论 ,得到了如下结果 :若对每个x∈V(X) ,图Yx 是非平凡的连通图 ,则X[Yx x∈V(X) ]是强不可缩回的充要条件是每个Yx 都是强不可缩回的 ;若对每个x∈V(X) ,图Yx 有两个连通分支 ,其中恰有一个分支是孤立点 ,则X[Yx x∈V(X) ]是强不可缩回的充要条件是每个Yx 及X都是强不可缩回的 .

Strong unretractive property of generalized lexicographic product of graphs is discussed.Two results are obtained:If every Y x is nontrivial connected graph,then X[Y xx∈V(X)] is strong unretractive if and only if every Y x is strong unretractive;If every Y x has exactly one isolated vertex and has just two connected components,then X[Y xx∈V(X)] is strong unretractive if and only if every Y x and X are strong unretractive.