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The Roman domatic number of a graph

✍ Scribed by S.M. Sheikholeslami; L. Volkmann

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 268 KB
Volume: 23
Category: Article
ISSN: 0893-9659
DOI: 10.1016/j.aml.2010.06.016

No coin nor oath required. For personal study only.

✦ Synopsis

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 { f 1 , f 2 , . . . , f d } of Roman dominating functions on G with the property that

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 d R (G).

In this work we initiate the study of the Roman domatic number in graphs and we present some sharp bounds for d R (G). In addition, we determine the Roman domatic number of some graphs.

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