The Graceful Graphs on Several Kinds of Union Graphs
Wei Li-xia, Zhang Kun-long · Acta Scientiarum Naturalium Universitatis Sunyatseni · 2008
To study the gracefulness of unconnected union graphs,several kinds of unconnected union graphs are given and the following results are obtained:for arbitrary positive integer n,m,let s be the greatest integer not greater than n/2,Pn be a path with n vertex,St(m)be a star tree with m+1 vertex,graph An be the join graph of complement of P2 and Pn,then for n≥2,the union of A2n and arbitrary a graceful graph with n-1 edges is a graceful graph;for n≥5,m≥s+2,the union of An and star tree St(m) is a graceful graph,therefore the union of An and star tree St(n) is a graceful grap;for n≥5,the union of An and arbitrary path Pn is a(n-s)-graceful graph.