PRODUCT-CORDIAL INDEX AND FRIENDLY INDEX OF REGULAR GRAPHS

Abstract. Let G = (V;E) be a connected simple graph. A labeling f : V ! Z2 induces two edge labelings f+; f : E ! Z2 dened by f+(xy) = f(x)+f(y) and f(xy) = f(x)f(y) for each xy 2 E. For i 2 Z2, let vf (i) = jf??1(i)j, ef+(i) = j(f+)??1(i)j and ef (i) = j(f)??1(i)j. A labeling f is called friendly if jvf (1)??vf (0)j  1. For a friendly labeling f of a graph G, the friendly index of G under f is dened by i+ f (G) = ef+(1) ?? ef+(0). The set fi+ f (G) j f is a friendly labeling ofGg is called the full friendly index set of G. Also, the product-cordial index of G under f is dened by if (G) = ef (1) ?? ef (0). The set fif (G) j f is a friendly labeling ofGg is called the full product-cordial index set of G. In this paper, 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 asked by Kwong, Lee and Ng in 2010; and those of cycles.