两类非连通图(P_2∨)∪St(m)及(P_2∨)∪T_n的优美性

The Gracefulness of Two Kinds of Unconnected Graphs (P_2∨)∪St(m) and (P_2∨)∪T_n

对自然数n,m,i∈N,设Ki表示i个顶点的完全图,Kn是Kn的补图,St(m)表示m+1个顶点的星形树,Tn为n个节点的优美树,Pn为n个节点的路,P2∨Kn是P2与Kn联图.给出非连通图(P2∨Kn)∪St(m)和(P2∨Kn)∪Tn,并论证了当n≥2时,这两类图都是优美图.

For natural numbers n,m,i∈N, let Ki be an ivertex complete graph, Knis the complementay graph of graph Kn, St(m) represents a m+1vertex star tree, Tn is a nvertex tree, Pn is a nvertex path, P2∨Kn is the join graph of P2 and Kn. The present paper presents two kinds of unconnected graphs (P2∨Kn)∪St(m) and (P2∨Kn)∪Tn, and proves that the two kinds of graphs are graceful graphs when n≥2.