SOME NEW RESULTS ON INTEGER ADDITIVE SET-VALUED SIGNED GRAPHS

Year 2019, Volume: 9 Issue: 3, 638 - 645, 01.09.2019

N. K. Sudev P. K. Ashraf K. A. Germina

Abstract

Let X denotes 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 f : V G → P X − {∅} such that the induced function f + : E G → P X − {∅} is defined by f + uv = f u + f v ; ∀ uv ∈ E G , where f u + f v is the sumset of f u and f v . An IASL of a signed graph is an IASL of its underlying graph G together with the signature σ defined by σ uv = −1 |f+ uv | ; ∀ uv ∈ E Σ . In this paper, we discuss certain characteristics of the signed graphs which admits certain types of integer additive set-labelings.

Keywords

Signed graphs, balanced signed graphs, clustering of signed graphs, integer additive set-labeled signed graphs, arithmetic integer additive set-labeled signed graphs.

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