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Results on the maximal Roman domination number in graphs | ||
Journal of New Researches in Mathematics | ||
مقاله 51، دوره 6، شماره 25، آذر و دی 2020، صفحه 197-208 اصل مقاله (495.64 K) | ||
نوع مقاله: research paper | ||
نویسندگان | ||
Maryam Kamalipashakolaee1؛ Hossein Abdollahzadeh Ahangar 1؛ Mehran Motiee1؛ Seyed Mahmoud Sheikholeslami2 | ||
1Department of Mathematics, Babol Noshirvani University of Technology, Babol, Iran | ||
2Department of Mathematics Azarbaijan Shahid Madani University Tabriz-Iran | ||
چکیده | ||
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 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 maximal Roman dominating function on a graph G is a Roman dominating function f such that V_0={w ∈V(G)│f(w)=0} is not a dominating set of G. The weight of maximal Roman dominating function is the value w(f)=f(V(G))=∑_(x∈V(G))▒〖f(x).〗 The maximal Roman dominating number γ_mR (G) of a graph G equals the minimum weight of a maximal Roman dominating function on G. In this paper, we continue the study of maximal Roman domination number. First, we characterize all graphs G of order n with g(G)≥6 for which γ_mR (G) =n-2, and then, we consider this property for some graphs with girth at most 5. | ||
کلیدواژهها | ||
Maximal dominating set؛ Roman dominating function؛ maximal Roman dominating function | ||
مراجع | ||
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