Gracefulness of Unconnected Graphs(P_1∨P_n)∪G_r,(P_1∨P_n)∪(P_3∨■_r) and W_n∪St(m)
Wei Li-xia · Journal of Jilin University(Science Edition) · 2007
The present paper deals with the gracefulness of three kinds of unconnected graphs(P1∨Pn)∪Gr,(P1∨Pn)∪(P3∨K-r) and Wn∪St(m),and proves the following results: for positive integers n and m,let s=,r=s-1,Gr be a graceful graph with r-edges,if n≥4,then the unconnected graphs(P1∨Pn)∪Gr and(P1∨Pn)∪(P3∨K-r) are both graceful graphs;if n≥3 and m≥s,then the unconnected graph Wn∪St(m) is a graceful graph,where Pn is an n-vertex path,Kn is an n-vertex complete graph,K-n is the complement of graph Kn,graph G1∨G2 is the join graph of G1 and G2,Wn is an(n+1)-vertex wheel graph and St(m) is an(m+1)-vertex star tree.