A Study on Semi-arithmetic Integer Additive Set-Indexers of Graphs

Abstract

An integer additive set-indexer is defined as 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. An integer additive set-indexer $f$ is said to be an arithmetic integer additive set-indexer if every element of $G$ are labeled by non-empty sets of non negative integers, which are in arithmetic progressions. An integer additive set-indexer $f$ is said to be a semi-arithmetic integer additive set-indexer if vertices of $G$ are labeled by non-empty sets of non negative integers, which are in arithmetic progressions, but edges are not labeled by non-empty sets of non negative integers, which are in arithmetic progressions. In this paper, we discuss about semi-arithmetic integer additive set-indexer and establish some results on this type of integer additive set-indexers.

10 pages. arXiv admin note: substantial text overlap with arXiv:1312.7674, arXiv:1312.7672