Full friendly index set — I

Abstract

Let G=(V,E) be a graph, a vertex labeling f:V→Z2 induces an edge labeling f∗:E→Z2 defined by f∗(xy)=f(x)+f(y) for each xy∈E. For each, i∈Z2 define vf(i)=|f−1(i)| and ef(i)=|f∗−1(i)|. We call f friendly if |vf(1)−vf(0)|≤1. The full friendly index set of G is the set of all possible values of ef(1)−ef(0), where f is friendly. In this paper, we study the full friendly index sets of some standard graphs such as the complete graph Kn, the cycle Cn, fans Fm and F2,m and the Cartesian product of P3 and Pn i.e. P3×Pn.