FULL FRIENDLY INDEX SETS OF SLENDER AND FLAT CYLINDER GRAPHS

Let G = (V;E) be a connected simple graph. A labeling f : V ! Z2 induces an edge labeling f : E ! Z2 dened by f(xy) = f(x)+f(y) for each xy 2 E. For i 2 Z2, let vf (i) = jf??1(i)j and ef (i) = jf??1(i)j. A labeling f is called friendly if jvf (1) ?? vf (0)j  1. The full friendly index set of G consists all possible dierences between the number of edges labeled by 1 and the number of edges labeled by 0. In recent years, full friendly index sets for certain graphs were studied, such as tori, grids P2  Pn, and cylinders Cm  Pn for some n and m. In this paper we study the full friendly index sets of cylinder graphs Cm  P2 for m  3, Cm  P3 for m  4 and C3  Pn for n  4. The results in this paper complement the existing results in literature, so the full friendly index set of cylinder graphs are completely determined.