Some Results on the Strong Roman Domination Number of Graphs

Let G=(V,E) be a finite and simple graph of order n and maximum‎ ‎degree Δ(G)‎. ‎A strong Roman dominating function on a‎ ‎graph  G  is a function  f‎:V (G)→{0‎, ‎1,… ,‎[Δ(G)/2 ]‎+ ‎1}  satisfying the condition that every‎ ‎vertex v for which  f(v)=0  is adjacent to at least one vertex  u ‎for which...

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Bibliographic Details
Published in:Mathematics interdisciplinary research (Online) 2020-09, Vol.5 (3), p.259-277
Main Authors: Akram Mahmoodi, Sakineh Nazari-Moghaddam, Afshin Behmaram
Format: Article
Language:English
Subjects:
domination
roman domination
roman domination number
strong roman domination
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Summary:Let G=(V,E) be a finite and simple graph of order n and maximum‎ ‎degree Δ(G)‎. ‎A strong Roman dominating function on a‎ ‎graph  G  is a function  f‎:V (G)→{0‎, ‎1,… ,‎[Δ(G)/2 ]‎+ ‎1}  satisfying the condition that every‎ ‎vertex v for which  f(v)=0  is adjacent to at least one vertex  u ‎for which‎ f(u) ≤ 1‎+ [(1/2)| N(u) ∩ V0| ], ‎where V0={v ∊ V | f(v)=0}. The minimum of the‎ values ∑v∊ V f(v), ‎taken over all strong Roman dominating‎ ‎functions f of G‎, ‎is called the strong Roman domination‎ ‎number  of G and is denoted by γStR(G)‎. ‎In this paper we‎ ‎continue the study of strong Roman domination number in graphs‎. ‎In‎ particular‎, ‎we present some sharp bounds for γStR(G) and‎ we determine the strong Roman domination number of some graphs‎.
ISSN:2476-4965
DOI:10.22052/mir.2020.225635.1205