The Gracefulness of Two Kinds of Unconnected Graphs(P_2∨■)(0,0,r_1,0,…,0,r_n)∪St(m)and(P_2∨■)(r_1+a,r_2,0,…,0)∪G_r
Baogen Xu · Acta Scientiarum Naturalium Universitatis Sunyatseni · 2012
For natural numbers n,m and i∈N,let Ki be an i-vertex complete graph,let Kn be the complement graph of graph Kn.A(m+1)-vertex star tree is represented by St(m).Let Gr be a graceful graph with r-edges,let Pn be a n-vertex path and let P2∨■ be the join graph of P2 and Kn.Two kinds of unconnected graphs(P2∨Kn)(r1,r2,0,…,0) ∪ St(m) and(P2 ∨■)(r1+a,r2,0,…,0) ∪ Gr are presented.It proves that the above two kinds of graphs are graceful graphs when n≥2.