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 edgelabeling f : e ! z2 dened by f(xy) = f(x)+f(y) for each xy 2 e. for i 2 z2, let vf (i) = jf??1(i)jand ef (i) = jf??1(i)j. a labeling f is called friendly if jvf (1) ?? vf (0)j  1. the full friendly index setof g consists all possible dierences between the number of edges labeled by 1 and the number of edgeslabeled by 0. in recent years, full friendly index sets for certain graphs were studied, such as tori, gridsp2  pn, and cylinders cm  pn for some n and m. in this paper we study the full friendly index setsof cylinder graphs cm  p2 for m  3, cm  p3 for m  4 and c3  pn for n  4. the results in thispaper complement the existing results in literature, so the full friendly index set of cylinder graphs arecompletely determined.