# Some New Results on Integer Additive Set-Valued Signed Graphs

@article{Sudev2016SomeNR, title={Some New Results on Integer Additive Set-Valued Signed Graphs}, author={Naduvath Sudev and P. K. Ashraf and K. A. Germina}, journal={arXiv: General Mathematics}, year={2016} }

Let $X$ denotes a set of non-negative integers and $\mathscr{P}(X)$ be its power set. An integer additive set-labeling (IASL) of a graph $G$ is an injective set-valued function $f:V(G)\to \mathscr{P}(X)-\{\emptyset\}$ such that the induced function $f^+:E(G) \to \mathscr{P}(X)-\{\emptyset\}$ is defined by $f^+(uv)=f(u)+f(v);\ \forall\, uv\in E(G)$, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. An IASL of a signed graph is an IASL of its underlying graph $G$ together with the signature…

## One Citation

A Study on Set-Valuations of Signed Graphs

- Mathematics
- 2016

Let $X$ be a non-empty ground set and $\mathcal{P}(X)$ be its power set. A set-labeling (or a set-valuation) of a graph $G$ is an injective set-valued function $f:V(G)\to \mathcal{P}(X)$ such that…

## References

SHOWING 1-10 OF 17 REFERENCES

A Study on Integer Additive Set-Valuations of Signed Graphs

- Mathematics
- 2015

Let $\N$ denote the set of all non-negative integers and $\cP(\N)$ be its power set. An integer additive set-labeling (IASL) of a graph $G$ is an injective set-valued function $f:V(G)\to…

A Study on Semi-arithmetic Integer Additive Set-Indexers of Graphs

- Mathematics
- 2014

A set-indexer of a graph $G$ is an injective set-valued function $f:V(G) \rightarrow2^{X}$ such that the function $f^{\oplus}:E(G)\rightarrow2^{X}-\{\emptyset\}$ defined by $f^{\oplus}(uv) =…

ON INTEGER ADDITIVE SET-INDEXERS OF GRAPHS

- Mathematics
- 2014

A set-indexer of a graph G is an injective set-valued function f : V (G)! 2 X such that the function f : E(G)! 2 X f;g dened by f (uv) = f(u)f (v) for every uv2E(G) is also injective, where 2 X is…

Additive Number Theory: Inverse Problems and the Geometry of Sumsets

- Mathematics
- 1996

Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer H -> 2, and tries to describe the structure of the sumset hA…

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…

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.…

A Dynamic Survey of Graph Labeling

- Mathematics
- 2009

A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years…

Signed Graphs and Geometry

- Mathematics
- 2013

These lecture notes are a personal introduction to signed graphs, concentrating on the aspects that have been most persistently interesting to me. They are just a few corners of signed graph theory;…

On signed paths , signed cycles and their energies

- Electron . J . Combin .
- 2015