The researches on gracefilness of two kinds of unconnected graphs
Zhang Kun-long · Journal of Shandong University · 2008
Two kinds of unconnected graphs(K2∨Cn)∪3i=1St(mi) and(K2∨C2n+k)∪St(m)∪G(k)n-1(k=1,2) were presented,and following results were proved: for natural number n,m,m1,m2,m3,let s=n2,n≥9,m1≥s+2,then graph(K2∨Cn)∪3i=1St(mi) is a graceful graph;for k=1,2,let n,m≥3,and let G(k)n-1 be a k-graceful graph with n-1 edges,then graph(K2∨C2n+k)∪St(m)∪G(k)n-1 is a graceful graph.Where K2 be a complete graph with 2 vertices,K2 is the complement of graph K2, graph K2∨Cn is the join graph of K2,and n-cycle Cn,St(m) is a star tree with m+1 vertices.