On Certain Types of Product Set-Labeling of Graphs

International audienceThe product set of two sets A and B of integers, denoted by A * B, is the set A * B = {ab : a ∈ A, b ∈ B}. For X ⊆ N, a product set-labeling (PS-labeling) of a graph G is an injective function ƒ : V (G) → P(X) such that the induced function f* : V (G) → P(X) is defined as ƒ*(uv) = ƒ(u) * ƒ(v)≤ uv ∈ E(G), ƒ(u) * ƒ(v) being the product set of ƒ(u) and ƒ(v). The PS-labeling of a graph can be classified into certain types in two ways: in accordance with the cardinalities of the set-labels and according to the nature of the collection of set-labels of elements of the graph G. This paper discusses different types of PS-labeling of graphs

On Integer Additive Set-Valuations of Finite Jaco Graphs

International audienceLet 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

A study on prime arithmetic integer additive set-indexers of graphs

International audienceLet N 0 be the set of all non-negative integers and P(N 0) be its power set. An integer additive set-indexer (IASI) is defined as an injective function f : V (G) → P(N 0) such that the induced function f + : E(G) → P(N 0) defined by f + (uv) = f (u)+f (v) is also injective, where N 0 is the set of all non-negative integers. A graph G which admits an IASI is called an IASI graph. An IASI of a graph G is said to be an arithmetic IASI if the elements of the set-labels of all vertices and edges of G are in arithmetic progressions. In this paper, we discuss about a particular type of arithmetic IASI called prime arithmetic IASI

A study on the product set-labeling of graphs

International audienc

On certain arithmetic integer additive set-indexers of graphs

International audienc