Gracefulness of the Graphs C4k∪Pn
Duan Zi · Journal of Yantai University · 2003
The gracefulness of C4k∪Pn,n≥k+2;which are the disjoint union graphs of cycles and pahts is discussed in this paper. With the concept of weak gracefulness,two propositions equivalent to the problem discussed are given, which simplifies the problem with the transition from proving the gracefulness of C4k∪Pn,n≥k+2,doing the weak gracefulness of paths. Using this method, the gracefulness of C4k∪Pn,n≥k+2;for k=2,3,4,5,6,7 is proved.