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Information Journal Paper

Title

Results on the maximal Roman domination number in graphs

Pages

  197-208

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 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.

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    APA: Copy

    Kamali pashakolaee, Maryam, ABDOLLAHZADEH AHANGAR, HOSSEIN, Motiee, Mehran, & Sheikholeslami, Seyed Mahmoud. (2020). Results on the maximal Roman domination number in graphs. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 6(25 ), 197-208. SID. https://sid.ir/paper/955435/en

    Vancouver: Copy

    Kamali pashakolaee Maryam, ABDOLLAHZADEH AHANGAR HOSSEIN, Motiee Mehran, Sheikholeslami Seyed Mahmoud. Results on the maximal Roman domination number in graphs. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2020;6(25 ):197-208. Available from: https://sid.ir/paper/955435/en

    IEEE: Copy

    Maryam Kamali pashakolaee, HOSSEIN ABDOLLAHZADEH AHANGAR, Mehran Motiee, and Seyed Mahmoud Sheikholeslami, “Results on the maximal Roman domination number in graphs,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 6, no. 25 , pp. 197–208, 2020, [Online]. Available: https://sid.ir/paper/955435/en

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