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On the forcing dimension of a graph

Bagheri Ghavam Abadi, B ; Sharif University of Technology | 2015

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  1. Type of Document: Article
  2. Publisher: Societatea de Stiinte Matematice din Romania , 2015
  3. Abstract:
  4. A set W ⊆ V (G) is called a resolving set, if for each two distinct vertices u, v ∈ V (G) there exists w ∈ W such that d(u, w) ≠ d(v, w), where d(x, y) is the distance between the vertices x and y. A resolving set for G with minimum cardinality is called a metric basis. The forcing dimension f(G, dim) (or f(G)) of G is the smallest cardinality of a subset S ⊂ V (G) such that there is a unique basis containing S. The forcing dimensions of some well-known graphs are determined. In this paper, among some other results, it is shown that for large enough integer n and all integers a, b with 0 ≤ a ≤ b ≤ n and b ≥ 1, there exists a nontrivial connected graph G of order n with f(G) = a and dim(G) = b if {a, b} ≠ {0, 1}
  5. Keywords:
  6. Basis number ; Forcing dimension ; Metric basis ; Resolving set
  7. Source: Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie ; Volume 58, Issue 2 , 2015 , Pages 129-136 ; 12203874 (ISSN)
  8. URL: http://ssmr.ro/bulletin/pdf/58-2/articol_1.pdf