A Class of Graceful Graphs
Xirong Xu · Journal of Mathematical Research and Exposition · 2004
Let u and ν be two fixed vertices. Connecting u and v by b internally disjoint paths of length a, the resulting graphs is denoted by Pa.b. KM. Kathiresan showed that P2r.2m-1 is graceful and conjectured that Pa.b is graceful except when (a,b) = (2r+1, 4s + 2). Y. S. Yang showed that P2r+1,2m-1 and P2r.2m (r= 1, 2, 3, 4) are graceful. In this paper, P2r.2m is proved to be graceful for r=5,6,7.