k-STRONG GRACEFULNESS OF JOIN GRAPH P_1VP_n
Zhou Jun-mei · Journal of Mathematics · 2010
In this article,we study the k-strong gracefulness for join graph P1V Pn.By using the definition of k-strong graceful graph,we obtain the necessary conditions for a join graph P1V Pn to be an k-strong graceful graph.It is proved that,for n = 2k-1,a join graph P1V Pn is an k-strong graceful graph and is also k graceful graph,and for n≥3,a join graph P1V Pn is a 2-strong graceful graph and also a 2-graceful graph.These extend the result of a join graph P1V Pn to be a graceful graph.