Publication

Abstract : pA set-indexer of a given graph G = (V, E) is an assignment f of distinct nonempty subsets of a finite nonempty 'ground set' X = {x1, x2,...,xn} of car dinality n, where 2X denotes the power set of X, to the vertices of G so that the values f ⊕(e), e = uv ∈ E; obtained as the symmetric differences f(u) ⊕ f(v) of the subsets f(u) and f(v) of X, are all distinct. It is well known that every graph admits a set-indexer. A function f : V∪ E → Y = 2X – {∅} is called a set-sequential labeling of G = (V, E) if it is a bijection and for all uv ∈E, f(u) ⊕ f(v) = f(uv): A graph is called set-sequential if it admits a set-sequential labeling. A set-indexer f of a graph G = (V, E) is called a set-graceful labeling of G if there exists a nonempty ground set X such that f⊕(E) = 2X − {∅} and G is setgraceful if it admits a set-graceful labeling. In this article we provide characterization of m copies of K2 , mK2 , that are set-sequential and the friendship graphs C3m, consisting of m triangles attached at one common vertex that are set-graceful. It is also established that for every set X of odd cardinality there is a set-sequential tree of diameter four./p