广义Mycielski图的补图的若干参数

Several parameters of the complement of generalized Mycielskian graph

为了寻找一类具有任意大色数但不含三角形的图类,Mycielski提出了一种有趣的图变换,称之为图G的Mycielskian图,记为μ(G).Lam等对μ(G)的定义做了一个自然的推广,提出了广义Mycielskian图(也被Tardif称为cones over图),记为μm(G),其中m代表正整数.本文中给出了广义Mycielskian图的补图的控制数、全控制数、packing数和open packing数的明确结果.

In a search for triangle-free graphs with arbitrarily large chromatic number,Mycielski has developed a graph transformation that transforms a graph G into a new graphμ(G),which is called the Mycielskian of G.A generalization of this transformation is the generalized Mycielskianμm(G),where m denotes a positive integer.This paper investigates the domination,total domination,packing and open packing of the complement of generalized Mycielskian graph.