article · Carpathian Mathematical Publications · 2015

A study on integer additive set-valuations of signed graphs

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Abstract

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-labeling (IASL) of a graph $G$ is an injective set-valued function $f:V(G)\to\mathcal{P}(\mathbb{N}_0)\setminus\{\emptyset\}$ such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)\setminus \{\emptyset\}$ is defined by $f^+(uv) = f(u)+ f(v)$, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. A graph which has an IASL is usually called an IASL-graph. An IASL $f$ of a graph $G$ is said to be an integer additive set-indexer (IASI) of $G$ if the associated function $f^+$ is also injective. In this paper, we define the notion of integer additive set-labeling of signed graphs and discuss certain properties of signed graphs which admits certain types of integer additive set-labelings.

Cite this paper

APA 7

Naduvath, S., & Germina, K. A. (2015). A study on integer additive set-valuations of signed graphs. Carpathian Mathematical Publications, 7(2), 236–246. https://doi.org/10.15330/cmp.7.2.236-246

MLA 9

Naduvath, Sudev, and K. A. Germina. “A study on integer additive set-valuations of signed graphs.” Carpathian Mathematical Publications, vol. 7, no. 2, 2015, pp. 236–46, https://doi.org/10.15330/cmp.7.2.236-246.

Chicago

Naduvath, Sudev, and K. A. Germina. 2015. “A study on integer additive set-valuations of signed graphs.” Carpathian Mathematical Publications 7 (2): 236–46. https://doi.org/10.15330/cmp.7.2.236-246.

Harvard

Naduvath, S. and Germina, K.A. (2015) ‘A study on integer additive set-valuations of signed graphs’, Carpathian Mathematical Publications, 7(2), pp. 236–246. Available at: https://doi.org/10.15330/cmp.7.2.236-246.

BibTeX

@article{naduvath2015study,
  title = {{A study on integer additive set-valuations of signed graphs}},
  author = {Naduvath, Sudev and Germina, K. A.},
  journal = {Carpathian Mathematical Publications},
  volume = {7},
  number = {2},
  pages = {236--246},
  year = {2015},
  doi = {10.15330/cmp.7.2.236-246}
}

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