Researches on gracefulness of graphs (P_1~(1)∨P_n)∪(P_1~(2)∨P_(2n)) and (P_2∨K_n)∪G_(n-1)
Zhang Kun-long · Journal of Hefei University of Technology · 2008
The present paper presents the three kinds of unconnected graphs(P_1∨P_n)∪St(m),(P_1(1)∨P_n)∪(P_1(2)∨P_2n) and(P_2∨K_n)∪G_n-1,proves following results:for natural number n,let s=,if n≥3 and m≥s then unconnected graph (P_1∨P_n)∪St(m) is a graceful graph;if n≥3 then unconnected graph (P_1(1)∨P_n)∪(P_1(2)∨P_2n) is an s-graceful graph,if n≥2 then unconnected graph(P_2∨K_n)∪G_n-1 is a graceful graph,where P_n is n-vertex path;P_1,P_1(1)and P_1(2) are trivial graphs;G_1∨G_2 is the join graph of G_1 and G_2;St(m) is(m+1)-vertex star tree;K_n is an n-vertex complete graph;K_n is the complement of graph K_n,G_n-1 is a graceful graph with n-1 edges.