On certain arithmetic integer additive set-indexers of graphs

Abstract

Let N 0 denote the set of all non-negative integers and P(N 0 ) be its power set. An integer additive set-indexer (IASI) of a graph G is an injective function f :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 two special types of arithmetic IASIs.Key words: Integer additive set-indexers, uniform integer additive set-indexers, arithmetic integer additive set-indexers, isoarithmetic integer additive set-indexers, biarithmetic integer additive set-indexer.

A note on sparing number algorithm of graphs

“…Let X be a non-empty finite set of non-negative integers and let P(X) be its power set. An integer additive set-labeling (IASL) of a graph G (see [4,7]) is an injective function f : V (G) → P(X) − {∅} such that the induced function…”

“…Certain studies on WIASL-graphs and their sparing numbers have been done in [4,7,8,9,10]. In this paper, we discuss an algorithm to determine the sparing number of arbitrary finite connected graphs.…”

A study on integer additive set-valuations of signed graphs

“…Let N 0 be the set of all non-negative integers and let X be a non-empty subset of X. Using the concepts of sumsets, we have the following notions as defined in [5,9].…”

Switched signed graphs of integer additive set-valued signed graphs

“…Let N 0 be the set of all non-negative integers and let X be a non-empty subset of N 0 . Using the concepts of sumsets, we have the following notions as defined in [6,10]. The cardinality of the set-label of an element (vertex or edge) of a graph G is called the set-indexing number of that element.…”

“…[6,10] An integer additive set-labeling (IASL, in short) is an injective function f :V (G) → P(X) − {∅} such that the induced function f + : E(G) → P(X) − {∅} is defined by f + (uv) = f (u) + f (v) ∀uv ∈ E(G).A graph G which admits an IASL is called an integer additive set-labeled graph (IASL-graph).…”