On the Odd Gracefulness of Cyclic Snakes With Pendant Edges

Graceful and odd gracefulness of a graph are two entirely different concepts. A graph may posses one orboth of these or neither. We present four new families of odd graceful graphs. In particular we show an oddgraceful labeling of the linear kC4 snake e mK1 and therefore we introduce the odd graceful labeling of4 1 kC snake e mK ( for the general case ). We prove that the subdivision of linear 3 kC snake is oddgraceful. We also prove that the subdivision of linear 3 kC snake with m-pendant edges is odd graceful.Finally, we present an odd graceful labeling of the crown graph n 1 P e mK .