A Note on Sparing Number Algorithm of Graphs

الأصل · EN

Let X denote a set of all non-negative integers and (X) be its power set. A weak integer additive set-labeling (WIASL) of a graph G is an injective set-valued function f:V(G)→ (X)-{} where induced function f+:E(G) → (X)-{} is defined by f+ (uv) = f(u)+ f(v) such that either |f+ (uv)|=|f(u)| or |f+ (uv)|=|f(v)|, where f(u)+f(v) is the sumset of f(u) and f(v). The sparing number of a WIASL-graph G is the minimum required number of edges in G having singleton set-labels. In this paper, we discuss an algorithm for finding the sparing number of arbitrary graphs.