A Note on the Sparing Number of Generalised Petersen Graphs

By : Germina Augustine, Chithra Kaithavalappil, Sudev Naduvath

Page No: 23-31

Abstract
Let X denote a set of non-negative integers and P(X) be its power set. An integer additive set-labeling (IASL) of a graph G is an injective set-valued function ƒ : V (G) ? P(X) – {?} where induced function ƒ+ : E (G) ? P(X) – {?} is defined by ƒ+(uv) = ƒ(u) + ƒ(v), whereƒ(u) + ƒ(v) is the sumset of ƒ(u) and ƒ(v). The cardinality of the set-label of an element of G is said to be the set-indexing number of that element. A weak integer additive set-labeling is an IASL, in which the set-indexing number of every edge is equal to the setindexing number of at least one of its end vertices. The sparing number of a graph G is the minimum number of edges having set indexing number 1 required for G to admit weak IASL. In this paper, we discuss the sparing number of certain generalised Petersen graphs.

Authors :
Sudev Naduvath : Department of Mathematics Vidya Academy of Science & Technology Thrissur, Kerala, India.
Chithra Kaithavalappil : Naduvath Mana, Nandikkara Thrissur, Kerala, India.
Germina Augustine : Department of Mathematics Central University of Kerala Kasaragod, India.