{
  "id": "1407.4869",
  "version": "v1",
  "published": "2014-07-18T02:00:10.000Z",
  "updated": "2014-07-18T02:00:10.000Z",
  "title": "The Sparing Number of the Cartesian Products of Certain Graphs",
  "authors": [
    "K. P. Chithra",
    "K. A. Germina",
    "N. K. Sudev"
  ],
  "comment": "8 pages, published. arXiv admin note: substantial text overlap with arXiv:1311.0858",
  "journal": "Communications in Mathematics and Applications, Vol.5 Issue 1, 2014, 23-30",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\mathbb{N}_0$ be the set of all non-negative integers. An integer additive set-indexer (IASI) is defined as an injective function $f:V(G)\\rightarrow \\mathcal{P}(\\mathbb{N}_0)$ such that the induced function $f^+:E(G) \\rightarrow \\mathcal{P}(\\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$ and $\\mathcal{P}(\\mathbb{N}_0)$ is the power set of $\\mathbb{N}_0$. If $f^+(uv)=k \\forall ~ uv\\in E(G)$, then $f$ is said to be a $k$-uniform integer additive set-indexer. An integer additive set-indexer $f$ is said to be a weak integer additive set-indexer if $|f^+(uv)|=max(|f(u)|,|f(v)|) \\forall ~ uv\\in E(G)$. In this paper, we study about the sparing number of the cartesian product of two graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-18T02:00:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C78"
    ],
    "keywords": [
      "cartesian product",
      "sparing number",
      "weak integer additive set-indexer",
      "uniform integer additive set-indexer",
      "power set"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.4869C"
    }
  }
}