ON FRIENDLY INDEX SETS OF TREES
Ebrahim Salehi, Sin-Min Lee · 2006
ABSTRACT. For a graph G = (V,E) and a coloring I: V(G)-t Z2 letv,(i) II-l(i)l. lissaidtobefriendlyiflv,(l)-v,(O)I:; l.The coloring J: V(G)-t Z2 induces an edge labeling r: E(G)-t Z2 defined by r(xy) f(x) + fey) Vxy E E(G), where the summation is done in Z2. Let e,(i) Ir-1 (i)l. The friendly index set of the graph G, denoted by FI(G), is defined by FICG) = {Ie,(l) e,(O)I: f is a friendly vertx labeling of G}. In this paper we will determine the friendly index set of certain classes of trees, which in turn will verify the validity of the conjecture that the elements of friendly index set of any tree form an arithmetic progression.