# On Integer Additive Set-Valuations of Finite Jaco Graphs

## Authors

• N. K. Sudev Department of Mathematics, Vidya Academy of Science & Technology, Thrissur
• K. P. Chithra Naduvath Mana, Nandikkara, Thrissur
• K. A. Germina Department of Mathematics, University of Botswana

## Keywords:

Integer additive set-labeled graphs, Weak integer additive set-labeled graphs, Arithmetic integer additive set-labeled graphs, Dispensing number of a graph, Finite linear Jaco graph

## Abstract

Let $$X$$ denote a set of non-negative integers and $$\mathcal{P}(X)$$ be its power set. An integer additive set-labeling (IASL) of a graph $$G$$ is an injective set-valued function $$f:V(G)\to \mathcal{P}(X)-\{\emptyset\}$$ where induced function $$f^+:E(G) \to \mathcal{P}(X)-\{\emptyset\}$$ is defined by $$f^+ (uv) = f(u)+ f(v)$$, where $$f(u)+f(v)$$ is the sumset of $$f(u)$$ and $$f(v)$$. Let $$f(x)=mx+c$$; $$m\in \mathbb{N}$$, $$c\in N_0$$. A finite linear Jaco graph, denoted by $$J_n(f(x))$$, is a directed graph with vertex set $$\{v_i: i\in \mathbb{N}\}$$ such that $$(v_i,v_j)$$ is an arc of $$J_n(f(x))$$ if and only if $$f(i)+i-d^-(v_j)\ge j$$. In this paper, we discuss the admissibility of different types of integer additive set-labeling by finite linear Jaco graphs.

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2016-05-24
CITATION

## How to Cite

Sudev, N. K., Chithra, K. P., & Germina, K. A. (2016). On Integer Additive Set-Valuations of Finite Jaco Graphs. Journal of Informatics and Mathematical Sciences, 8(2), 113–121. https://doi.org/10.26713/jims.v8i2.408

## Section

Research Articles