{
  "id": "1401.5164",
  "version": "v1",
  "published": "2014-01-21T03:22:36.000Z",
  "updated": "2014-01-21T03:22:36.000Z",
  "title": "Metric Dimension of Amalgamation of Regular Graphs",
  "authors": [
    "Rinovia Simanjuntak",
    "Danang Tri Murdiansyah"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A set of vertices $S$ resolves a graph $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $S$. The metric dimension of $G$ is the minimum cardinality of a resolving set of $G$. Let $\\{G_1, G_2, \\ldots, G_n\\}$ be a finite collection of graphs and each $G_i$ has a fixed vertex $v_{0_i}$ or a fixed edge $e_{0_i}$ called a terminal vertex or edge, respectively. The vertex-amalgamation of $G_1, G_2, \\ldots, G_n$, denoted by $Vertex-Amal\\{G_i;v_{0_i}\\}$, is formed by taking all the $G_i$'s and identifying their terminal vertices. Similarly, the edge-amalgamation of $G_1, G_2, \\ldots, G_n$, denoted by $Edge-Amal\\{G_i;e_{0_i}\\}$, is formed by taking all the $G_i$'s and identifying their terminal edges. Here we study the metric dimensions of vertex-amalgamation and edge-amalgamation for finite collection of regular graphs: complete graphs and prisms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-21T03:22:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C12"
    ],
    "keywords": [
      "metric dimension",
      "regular graphs",
      "finite collection",
      "minimum cardinality",
      "complete graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.5164S"
    }
  }
}