  An odd graceful labeling of a graph G=(V,E) is a function
f:V(G)->[0,1,2,...,2|E(G)|-1} such that |f(u)-f(v)| is odd value less than or
equal to 2|E(G)-1| for any u, v in V(G). In spite of the large number of papers
published on the subject of graph labeling, there are few algorithms to be used
by researchers to gracefully label graphs. This work provides generalized odd
graceful solutions to all the vertices and edges for the tensor product of the
two paths P_n and P_m denoted P_n^P_m . Firstly, we describe an algorithm to
label the vertices and the edges of the vertex set V(P_n^P_m) and the edge set
E(P_n^P_m) respectively. Finally, we prove that the graph P_n^P_m is odd
graceful for all integers n and m.

Discrete Mathematics