A study on integer additive set-valuations of signed graphs
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...
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2015-12-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Subjects: | |
| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/1403 |
| _version_ | 1818213788440068096 |
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| author | N.K. Sudev K.A. Germina |
| author_facet | N.K. Sudev K.A. Germina |
| author_sort | N.K. Sudev |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-12T06:09:51Z |
| format | Article |
| id | doaj.art-f2cae270c5ec4c0ba197c924b3be3fe2 |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-12-12T06:09:51Z |
| publishDate | 2015-12-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-f2cae270c5ec4c0ba197c924b3be3fe22022-12-22T00:35:12ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102015-12-017223624610.15330/cmp.7.2.236-2461403A study on integer additive set-valuations of signed graphsN.K. Sudev0K.A. Germina1Department of Mathematics, Vidya Academy of Science and Technology, 680501, Thrissur, IndiaDepartment of Mathematics, University of Botswana, 4775 Notwane Rd., Private Bag UB 0022, Gaborone, BotswanaLet $\mathbb{N}_0$ 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.https://journals.pnu.edu.ua/index.php/cmp/article/view/1403signed graphsbalanced signed graphsclustering of signed graphsiasl-signed graphsstrong iasl-signed graphsweak iasl-signed graphsisoarithmetic iasl-signed graphs |
| spellingShingle | N.K. Sudev K.A. Germina A study on integer additive set-valuations of signed graphs Karpatsʹkì Matematičnì Publìkacìï signed graphs balanced signed graphs clustering of signed graphs iasl-signed graphs strong iasl-signed graphs weak iasl-signed graphs isoarithmetic iasl-signed graphs |
| title | A study on integer additive set-valuations of signed graphs |
| title_full | A study on integer additive set-valuations of signed graphs |
| title_fullStr | A study on integer additive set-valuations of signed graphs |
| title_full_unstemmed | A study on integer additive set-valuations of signed graphs |
| title_short | A study on integer additive set-valuations of signed graphs |
| title_sort | study on integer additive set valuations of signed graphs |
| topic | signed graphs balanced signed graphs clustering of signed graphs iasl-signed graphs strong iasl-signed graphs weak iasl-signed graphs isoarithmetic iasl-signed graphs |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/1403 |
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