The sparing number of certain graph powers

Title

The sparing number of certain graph powers

Creator

Sudev N.K.; Chithra K.P.; Germina K.A.

Description

Let N0 be the set of all non-negative integers and P(N0) be its power set. Then, 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) deffned by f+(uv) = f(u) + f(v) is also injective. An IASI f is said to be a weak IASI if jf+(uv)j = 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 set-indexing number of an element of a graph G, a vertex or an edge, is the cardinality of its set-labels. 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 study the admissibility of weak IASI by certain graph powers and their corresponding sparing numbers. 2019 Sciendo. All rights reserved.

Source

Acta Universitatis Sapientiae, Mathematica, Vol-11, No. 1, pp. 186-202.

Date

2019-01-01

Publisher

Sciendo

Subject

graph powers; integer additive set-indexers; mono-indexed elements of a graph; sparing number of a graph; weak integer additive set-indexers

Coverage

Sudev N.K., Department of Mathematics, CHRIST (Deemed to Be University), Bangalore, 560029, India; Chithra K.P., Department of Mathematics, CHRIST (Deemed to Be University), Bangalore, 560029, India; Germina K.A., Department of Mathematics, Central University of Kerala, Kasaragod, India

Rights

All Open Access; Gold Open Access; Green Open Access

Relation

ISSN: 18446094

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.2478/ausm-2019-0015

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