# Weak Integer Additive Set-Indexers of Certain Graph Operations

@article{Sudev2013WeakIA, title={Weak Integer Additive Set-Indexers of Certain Graph Operations}, author={Naduvath Sudev and K. A. Germina}, journal={arXiv: Combinatorics}, year={2013} }

An integer additive set-indexer is defined as an injective function $f:V(G)\rightarrow 2^{\mathbb{N}_0}$ such that the induced function $g_f:E(G) \rightarrow 2^{\mathbb{N}_0}$ defined by $g_f (uv) = f(u)+ f(v)$ is also injective, where $f(u)+f(v)$ is the sum set of $f(u)$ and $f(v)$ and $\mathbb{N}_0$ is the set of all non-negative integers. If $g_f(uv)=k \forall uv\in E(G)$, then $f$ is said to be a $k$-uniform integer additive set-indexers. An integer additive set-indexer $f$ is said to be a… Expand

#### 8 Citations

A Note on the Sparing Number of Graphs

- Mathematics
- 2014

An integer additive set-indexer is defined as an injective function $f:V(G)\rightarrow 2^{\mathbb{N}_0}$ such that the induced function $g_f:E(G) \rightarrow 2^{\mathbb{N}_0}$ defined by $g_f (uv) =… Expand

A Note on the Sparing Number of the Sieve Graphs of Certain Graphs

- Mathematics
- 2015

Let $\mathbb{N}_0$ denote the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-indexer (IASI) of a given graph $G$ is an injective function… Expand

Further Studies on the Sparing Number of Graphs

- Mathematics
- 2014

Let $\mathbb{N}_0$ denote the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-indexer is an injective function $f:V(G)\to… Expand

Weak Integer Additive Set-Indexed Graphs: A Creative Review

- Mathematics
- 2014

For a non-empty ground set $X$, finite or infinite, the {\em set-valuation} or {\em set-labeling} of a given graph $G$ is an injective function $f:V(G) \to \mathcal{P}(X)$, where $\mathcal{P}(X)$ is… Expand

Weak Set-Labeling Number of Certain Integer Additive Set-Labeled Graphs

- Computer Science
- 2015

The notion of theWeak set-labeling number of a graph G is introduced as the minimum cardinality of X so that G admits a WIASL with respect to the ground set X and the weak set- labeling numbers of certain graphs are discussed. Expand

On Weak Integer Additive Set-Indexers of Certain Graph Classes

- Mathematics
- 2014

Abstract Let ℕ0 denote the set of all non-negative integers and P (ℕ0) be its power set. An integer additive set-indexer (IASI) of a graph G is an injective function f : V (G) → P (ℕ0) such that the… Expand

The sparing number of certain graph powers

- Mathematics
- Acta Universitatis Sapientiae, Mathematica
- 2019

Abstract Let ℕ0 be the set of all non-negative integers and 𝒫(ℕ0) be its power set. Then, an integer additive set-indexer (IASI) of a given graph G is an injective function f : V(G) → P(ℕ0) such… Expand

Some New Results on Weak Integer Additive Set-Indexers of Graph Powers

- Mathematics
- 2014

An integer additive set-indexer is defined as an injective function $f:V(G)\rightarrow 2^{\mathbb{N}_0}$ such that the induced function $g_f:E(G) \rightarrow 2^{\mathbb{N}_0}$ defined by $g_f (uv) =… Expand

#### References

SHOWING 1-10 OF 11 REFERENCES

A Characterisation of weak integer additive Set-Indexers of graphs

- Mathematics
- 2013

An integer additive set-indexer is defined as an injective function f : V(G) → 2 N0 such that the induced function gf : E(G) → 2 N0 defined by gf(uv) = f(u)+ f(v) is also injective. An integer… Expand

On Weakly Uniform Integer Additive Set-Indexers of Graphs

- Mathematics
- 2013

We have the notion of set-indexers, integer additive set-indexers and k-uniform integer additive set-indexers of graphs. In this paper, we initiate a study of the graphs which admit k-uniform integer… Expand

Introduction to Graph Theory

- Mathematics
- 1995

1. Fundamental Concepts. What Is a Graph? Paths, Cycles, and Trails. Vertex Degrees and Counting. Directed Graphs. 2. Trees and Distance. Basic Properties. Spanning Trees and Enumeration.… Expand

Strongly Indexable Graphs: Some New Perspectives

- Mathematics
- 2013

Given any positive integer k , a ) , ( q p -graph ) , ( = E V G is strongly k -indexable if there exists a bijection

Introduction to Graph Theory

- Computer Science
- 2004

Gary Chartrand and Ping Zhang's lively and engaging style, historical emphasis, unique examples and clearly-written proof techniques make it a sound yet accessible text that stimulates interest in an evolving subject and exploration in its many applications. Expand

Graph Theory with Applications to Engineering and Computer Science (Prentice Hall Series in Automatic Computation)

- Computer Science
- 1974

This outstanding introductory treatment of graph theory and its applications has had a long life in the instruction of advanced undergraduates and graduate students in all areas that require knowledge of this subject. Expand

Graph Theory

- Computer Science
- 1997

Gaph Teory Fourth Edition is standard textbook of modern graph theory which covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each chapter by one or two deeper results. Expand

Integer Additive Set - Indexers of a Graph : Sum Square Graphs

- Journal of Combinatorics , Information and System Sciences
- 2012