EDGE-ODD GRACEFUL LABELINGS OF SOME PRISMS AND PRISM-LIKE GRAPHS
Abstract
A simple graph G with q edges is called anedge-odd graceful graph, EOGG, if there is a bijection f from the edge set of the graph to the set {1,3,5,...,2q−1} such that, when each vertex is assigned the sum of all values of the edges incident to it modulo 2q, 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, thenPrism( Wn) is an EOGG.