EDGE-ODD GRACEFUL LABELINGS OF SOME PRISMS AND PRISM-LIKE GRAPHS.

Abstract

A simple graph G with q edges is called an edge-odd graceful graph,

EOGG, if there is a bijection f from the edge set of the graph to the set

{ values of the edges incident to it modulo 2 1, 3, 5,..., 2q−1} such that, when each vertex is assigned the sum of all q, the resulting vertex labels

are distinct.

In this paper, we define new graphs called a prism of star Sn, Prism(Sn),

a prism-like graph, Prism3(Sn), and a prism of wheel graph Wn, Prism(Wn).

We give necessary conditions on n that force these graphs to be EOGG,

namely, (i) if n ≥ 3, then Prism(Sn) is an EOGG; (ii) if n ≥ 3 and

n ≡ 2 (mod 6), then Prism3(Sn) is an EOGG; (iii) if n ≥ 3 and 2|n, then

Prism(Wn) is an EOGG.