Abstract
Abstract. Let G = (V;E) be a connected simple graph. A labeling f : V !Z 2 induces two edgelabelings f + ;f : E !Z 2 de ned by f + (xy) = f(x)+f(y) and f (xy) = f(x)f(y) for each xy 2E. Fori 2Z 2 , let v f (i) = jf 1 (i)j, e f + (i) = j(f + ) 1 (i)jand e f (i) = j(f ) 1 (i)j. A labeling f is called friendlyif jv f (1) v f (0)j1. For a friendly labeling f of a graph G, the friendly index of G under f is de nedby i +f (G) = e + (1) e f + (0). The set fi +f (G) jf is a friendly labeling ofGgis called the full friendlyindex set of G. Also, the product-cordial index of G under f is de ned by i f (G) = e f (1) e (0).The set fi f (G) jf is a friendly labeling ofGgis called the full product-cordial index set of G. In thispaper, we nd a relation between the friendly index and the product-cordial index of a regular graph.As applications, we will determine the full product-cordial index sets of torus graphs which was askedby Kwong, Lee and Ng in 2010; and those of cycles. 1. IntroductionIn this paper, all graphs are simple and connected. All unde ned symbols and concepts may belooked up from [1]. Let G = (V;E) be a connected simple graph. A labeling f : V !Z
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