考虑含有完全图 K4的图的补图的L (2 ,1 )-标号的岛序列

摘要

In this paper ,the existence of connected graphs with at least two different island sequences is studied .Based on the relation between the minmum path coverings number of a class of graphs containg complete graph K4 and no adjacent heavy vertex except in K4 andλ-number and hole index of GC in L(2 ,1)-labeling .The result is obtained that the complement of this class of graphs possess two λ-labelings with the hole index ρ(G)≥1 and with different ordered sequences of island cardinalities .Finally the connectivity of complement of graph G is proved .%为了得到容许至少两个不同岛序列的连通图 ,文中考虑一类含有完全图 K4 且除K4 外不含相邻重点的图G的两个最小路覆盖数c(G)和其补图的两个 L(2 ,1)-标号下的λ数和洞指数ρ(GC )之间的关系 ,得到了其补图的两个不同 L (2 ,1 )-标号容许两个不同的岛序列且洞指数ρ(G)≥1的λ-标号,证明图GC 是连通的 .