On full friendly index sets of twisted product of Mobius ladders

Let G he a graph with vertex set V(G) and edge set E(G), a vertex labeling f : V (G) -> Z(2) induces an edge labeling f* : E(G) -> Z(2) defined by f* (x, y) = f (x) + f(y), for each edge (x,y) is an element of E(G). For each i is an element of Z(2), let v(f)(i) = vertical bar{v is an element of V(G) : f(v) = i}vertical bar and e(f)(i) =vertical bar{e is an element of E(G) : f* (e) = ill. A vertex labeling f of a graph G is said to he friendly if vertical bar v(f) (1) - v(f) (0)vertical bar <= 1. The friendly index set of the graph G, denoted by FI(G), is defined as {vertical bar e(f) (1) - e(f) (0)vertical bar : the vertex labeling f is friendly}. The full friendly index set of the graph G, denoted by FFI(G), is defined as {e(f) (1) - e(f) (0): the vertex labeling f is friendly}. In this paper, we determine FFI(G) and FI(G) for a class of cubic graphs which are twisted product of Mobius.