TY - JOUR
AU - Sudev, N. K.
AU - Chithra, K. P.
AU - Germina, K. A.
PY - 2016/05/24
Y2 - 2024/07/12
TI - On Integer Additive Set-Valuations of Finite Jaco Graphs
JF - Journal of Informatics and Mathematical Sciences
JA - Jour. Inform. Math. Sci.
VL - 8
IS - 2
SE - Research Articles
DO - 10.26713/jims.v8i2.408
UR - http://www.rgnpublications.com/journals/index.php/jims/article/view/408
SP - 113-121
AB - 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.
ER -