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IPM
30
YEARS OLD

“School of Mathematics”

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Paper   IPM / M / 11516
School of Mathematics
  Title:   The Roman domatic number of a graph
  Author(s):  S. M. Sheikholeslami (Joint with L. Volkmann)
  Status:   Published
  Journal: Appl. Math. Lett.
  Vol.:  23
  Year:  2010
  Pages:   1295-1300
  Supported by:  IPM
  Abstract:
A Roman dominating function on a graph G is a labeling f : V(G) → {0,1,2} such that every vertex with label 0 has a neighbor with label 2. A set {f1,f2,...,fd} of Roman dominating functions on G with the property that Σi=1dfi(v) ≤ 2 for each vV(G) is called a Roman dominating family (of functions) on G. The maximum number of functions in a Roman dominating family on G is the Roman domatic number of G, denoted by dR(G). this work we initiate the study of the Roman domatic number in graphs and we present some sharp bounds for dR(G). In addition, we determine the Roman domatic number of some graphs.

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