{
  "id": "1407.4533",
  "version": "v2",
  "published": "2014-07-17T01:17:31.000Z",
  "updated": "2015-03-18T10:47:02.000Z",
  "title": "A Study on Topological Integer Additive Set-Labeling of Graphs",
  "authors": [
    "N. K. Sudev",
    "K. A. Germina"
  ],
  "comment": "16 pages, 7 figures, Accepted for publication. arXiv admin note: text overlap with arXiv:1403.3984",
  "journal": "ELectronic Journal of Graph Theory and Applications, Vol. 3, Issue.1, 2015, pp. 70-84",
  "categories": [
    "math.CO"
  ],
  "abstract": "A set-labeling of a graph $G$ is an injective function $f:V(G)\\to \\mathcal{P}(X)$, where $X$ is a finite set and a set-indexer of $G$ is a set-labeling such that the induced function $f^{\\oplus}:E(G)\\to \\mathcal{P}(X)-\\{\\emptyset\\}$ defined by $f^{\\oplus}(uv) = f(u){\\oplus}f(v)$ for every $uv{\\in} E(G)$ is also injective. Let $G$ be a graph and let $X$ be a non-empty set. A set-indexer $f:V(G)\\to \\mathcal{P}(X)$ is called a topological set-labeling of $G$ if $f(V(G))$ is a topology of $X$. An integer additive set-labeling is an injective function $f:V(G)\\to \\mathcal{P}(\\mathbb{N}_0)$, whose associated function $f^+:E(G)\\to \\mathcal{P}(\\mathbb{N}_0)$ is defined by $f(uv)=f(u)+f(v), uv\\in E(G)$, where $\\mathbb{N}_0$ is the set of all non-negative integers and $\\mathcal{P}(\\mathbb{N}_0)$ is its power set. An integer additive set-indexer is an integer additive set-labeling such that the induced function $f^+:E(G) \\to \\mathcal{P}(\\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective. In this paper, we extend the concepts of topological set-labeling of graphs to topological integer additive set-labeling of graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-17T01:17:31.000Z",
      "comment": "14 pages, 7 figures, submitted. arXiv admin note: text overlap with arXiv:1403.3984",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-03-18T10:47:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C78"
    ],
    "keywords": [
      "topological integer additive set-labeling",
      "injective function",
      "induced function",
      "finite set",
      "non-empty set"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.4533S"
    }
  }
}