Results on the maximal Roman domination number in graphs

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Kamali pashakolaee Maryam; ABDOLLAHZADEH AHANGAR HOSSEIN; Motiee Mehran; Sheikholeslami Seyed Mahmoud

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Journal Paper

Paper Information

Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2020 | Volume:6 | Issue:25 Page(s): 197-208

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Title

Results on the maximal Roman domination number in graphs

Author(s)

Kamali pashakolaee Maryam | ABDOLLAHZADEH AHANGAR HOSSEIN | Motiee Mehran | Sheikholeslami Seyed Mahmoud | Issue Writer Certificate

Keywords

Maximal dominating set

Roman dominating function

maximal Roman dominating function

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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