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A note on the roman bondage number of planar graphs

Akbari, S ; Sharif University of Technology | 2013

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  1. Type of Document: Article
  2. DOI: 10.1007/s00373-011-1129-8
  3. Publisher: 2013
  4. Abstract:
  5. A Roman dominating function on a graph G = (V(G), E(G)) is a labelling f: (V(G) → {0, 1, 2} satisfying the condition that every vertex with label 0 has at least a neighbour with label 2. The Roman domination number γR(G) of G is the minimum of σv∈V(G)f(v) over all such functions. The Roman bondage number bR(G) of G is the minimum cardinality of all sets for which γR(G E) > γR(G). Recently, it was proved that for every planar graph P, bR(P) ≤ Δ(P) + 6, where Δ(P) is the maximum degree of P. We show that the Roman bondage number of every planar graph does not exceed 15 and construct infinitely many planar graphs with Roman bondage number equal to 7
  6. Keywords:
  7. Roman bondage number ; Roman domination number
  8. Source: Graphs and Combinatorics ; Volume 29, Issue 3 , 2013 , Pages 327-331 ; 09110119 (ISSN)
  9. URL: http://link.springer.com/article/10.1007%2Fs00373-011-1129-8