Arithmetic Intger Additive Set-Idexers of Graph Operations

TL;DR

This paper studies arithmetic integer additive set-indexers (IASIs) on graphs, focusing on their existence under various graph operations and products, contributing to the understanding of graph labelings with arithmetic progressions.

Contribution

It investigates the conditions under which graphs admit arithmetic IASIs when subjected to specific graph operations and products, expanding the theory of graph labelings.

Findings

Characterization of arithmetic IASIs for certain graph operations

Conditions for the existence of arithmetic IASIs in graph products

Extension of set-indexer theory to new graph classes

Abstract

An integer additive set-indexer is an injective function $f:V(G)\to 2^{\mathbb{N}_0}$ such that the induced function $g_f:E(G) \to 2^{\mathbb{N}_0}$ defined by $g_f (uv) = f(u)+ f(v)$ is also injective. A graph $G$ which admits an IASI is called an IASI graph. An arithmetic integer additive set-indexer is an integer additive set-indexer $f$, under which the set-labels of all elements of a given graph $G$ are arithmetic progressions. In this paper, we discuss about admissibility of arithmetic integer additive set-indexers by certain graph operations and certain products of graphs.