On Integer Additive Set-Valuations of Finite Jaco Graphs

Overview & Synopsis

Let X denote a set of non-negative integers and 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) → P (X ) −{;} where induced function f + : E(G) → P (X ) − {;} 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 ∈ N , c ∈ N 0 . A finite linear Jaco graph, denoted by J n ( f (x)), is a directed graph with vertex set { v i : i ∈ 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 ) ≥ j. In this paper, we discuss the admissibility of different types of integer additive set-labeling by finite linear Jaco graphs.