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Odd Graceful Labelings of Crown Graphs

1st International Conference Computer Science from Algorithms to Applications 01/2009;

ABSTRACT A graph G of size q is odd-graceful, if there is an injection f from V(G) to {0, 1, 2, …, 2q-1} such that, when each edge xy is assigned the label or weight | f(x) - f(y)|, the resulting edge labels are {1, 3, 5, …, 2q-1}. This definition was introduced in 1991 by Gnanajothi [1] who proved that the graphs obtained by joining a single pendant edge to each vertex of are odd graceful, if and only if n is even. In this paper we generalize Gnanajothi's result on cycles by showing that the graphs obtained by joining m pendant edges to each vertex of Cn are odd graceful if and only if n is even

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    ABSTRACT: A difference vertex labeling of a graph G an assignment of labels to the vertex of G that induces for each edge xy the weight | (x) - (y)|. A difference vertex labeling of a graph G of size n is odd-graceful if is an injection from V(G) to {0, 1, 2, …, 2q-1} such that the induced weights are {1, 3, 5, …, 2q-1}. In this paper, we present odd graceful labelings of some graphs. In particular we show, odd graceful labelings of the kC4- snakes ( for the general case), kC8 and kC12- snakes ( for even case). We also prove that the linear kCn- snakes is odd graceful if and only if n and k are even.
    Electronic Journal of Nonlinear Analysis and Application. 12/2012; 6:115-119.

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