A Note On The Sparing Number Of The Sieve Graphs Of Certain Graphs

Sudev Naduvath (1) , Augustine Germina (2)

1 Christ University, Bangalore, India
2 CUK - Central University of Kerala

Let N0 denote the set of all non-negative integers and P(N0) be its power set. An integer additive set-indexer (IASI) of a given graph G is an injective function f : V (G) ! P(N0) such that the induced function f + : E(G) ! P(N0) de…ned by f + (uv) = f (u) + f (v) is also injective. An IASI f of a graph G is said to be a weak IASI of G if f + (uv) = max(jf (u)j; jf (v)j) for all u; v 2 V (G). A graph which admits a weak IASI may be called a weak IASI graph. The sparing number of a graph G is the minimum number of edges with singleton set-labels required for a graph G to admit a weak IASI. In this paper, we introduce the notion of k-sieve graphs of a given graph and study their sparing numbers.

Domaines: Mathématiques [math]; Combinatoire [math.CO]

Sudev Naduvath, Augustine Germina. A Note On The Sparing Number Of The Sieve Graphs Of Certain Graphs. Applied Mathematics E - Notes, 2015. ⟨hal-02263323⟩