An Algorithm for Odd Graceful Labeling of the Union of Paths and Cycles

Details An Algorithm for Odd Graceful Labeling of the Union of Paths and Cycles An Algorithm for Odd Graceful Labeling of the Union of Paths and Cycles

2010-03-18

arxiv.org/abs/1003.3566v1

International journal on applications of graph theory in wireless ad hoc networks and sensor networks 2.1 (2010) 112-119

Computer Science

Networking and Internet Architecture

9 Pages, JGraph-Hoc Journal

Scientific paper

10.5121/jgraphhoc.2010.2108

In 1991, Gnanajothi [4] proved that the path graph P_n with n vertex and n-1 edge is odd graceful, and the cycle graph C_m with m vertex and m edges is odd graceful if and only if m even, she proved the cycle graph is not graceful if m odd. In this paper, firstly, we studied the graph C_m $\cup$ P_m when m = 4, 6,8,10 and then we proved that the graph C_ $\cup$ P_n is odd graceful if m is even. Finally, we described an algorithm to label the vertices and the edges of the vertex set V(C_m $\cup$ P_n) and the edge set E(C_m $\cup$ P_n).

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