The graceful labeling of two classes disjoint union graph
Zhang Zhi-shang · Journal of Northeast Normal University · 2013
The present paper deals with the gracefulness of unconnected graph,and proves the following results:let G is a graceful bipartite graph with q edges,gracefu labeling of G is θ,a=max{k|0kq,k≠θ(v),v∈V(G)},b=min{k|0kq,k≠θ(v),v∈V(G)},h=min{q-a,b},Pm is a path with m edges,(1) when m=2n-1 or m≥2n+h,then the graph(2n)G∪Pm be a graceful graph.(2) when q is odd,then(q+2)G be a graceful graph.