Friendly Index Sets and Friendly Index Numbers of Some Graphs
Pradeep G. Bhat, Devadas C Nayak · viXra · 2014
Let G be a graph with vertex set V (G) and edge set E(G). Consider the set A = {0, 1}. A labeling f : V (G) ! A, induces a partial edge labeling f� : E(G) ! A, defined by f�(xy) = f(x) if and only if f(x) = f(y) for each edge xy 2 E(G). For i 2 A, let vf (i) = |{v 2 V (G) : f(v) = i}| and we denote eBf∗ (i) = |{e 2 E(G) : f�(e) = i}|. In this paper we define friendly index number(FIN) and full friendly index number(FFIN) of graph G as the cardinality of the distinct elements of friendly index set and full friendly index set respectively and obtaining these numbers along with their sets of some families graphs.