Abstract
Graceful and odd gracefulness of a graph are two entirely different concepts. A graph may posses one or both of these or neither. We present four new families of odd graceful graphs. In particular we show an odd graceful labeling of the linear 4 1 kC snake mK - e and therefore we introduce the odd graceful labeling of 4 1 kC snake mK - e ( for the general case ). We prove that the subdivision of linear 3 kC snake - is odd graceful. 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 1 n P mK e .
Highlights
The graphs considered here will be finite, undirected and simple
We denote the crown graphs by C n K1, the crown graphs by C n mK1
We denote the crown snakes by kC n − snake e mK1
Summary
The graphs considered here will be finite, undirected and simple. The symbols V(G) and E(G) will denote the vertex set and edge set of a graph G respectively. p and q denote the number of vertices and edges of G respectively.A graph G of size q is odd-graceful, if there is an injection φ from V(G) to {0, 1, 2, ..., 2q-1} such that, when each edge xy is assigned the label or weight |φ (x) - φ (y)|, the resulting edge labels are {1, 3, 5, ..., 2q-1}. Odd graceful labeling, path, cyclic snakes, pendant edges. Definition 1.2 The kCn-snake is called linear, if the block-cut-vertex graph of kCn-snake has the property that the distance between any two consecutive cut-vertices is
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