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

2014/03/25 by N K Sudev, K A Germina · 2 citations
Mathematics · #math.CO #msc:05C78

paper · pdf

published as International Journal of Mathematical Sciences & Engineering Applications, Vol.8, No.III, 2014, pp. 157-165 · 10 pages. arXiv admin note: substantial text overlap with arXiv:1312.7674, arXiv:1312.7672

arxiv created 2014/03/25 · arxiv updated 2014/06/10

Abstract

An integer additive set-indexer is defined as an injective function f:V(G)→ 2^ℕ₀ such that the induced function g_f:E(G) → 2^ℕ₀ 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.

Citations

• A Study on Arithmetic Integer Additive Set-Indexers of Graphs
• On Integer Additive Set-Indexers of Graphs

Cited by

• A Study on Prime Arithmetic Integer Additive Set-Indexers of Graphs
• On Certain Arithmetic Integer Additive set-indexers of Graphs