A Roman dominating function (RDF) on a graph G=(V,E) is a function f : V → {0, 1, 2} such that every vertex u for which f(u)=0 is adjacent to at least one vertex v for which f(v)=2. An RDF f is called an outer independent Roman dominating function (OIRDF) if the set of vertices assigned a 0 under f is an independent set. The weight of an OIRDF is the sum of its function values over all vertices, and the outer independent Roman domination number ΥoiR (G) is the minimum weight of an OIRDF on $G$. In this paper, we show that if T is a tree of order n ≥ 3 with s(T) support vertices, then $gamma _{oiR}(T)leq min { frac{5n}{6},frac{3n+s(T)}{4}}.$ Moreover, we characterize the tress attaining each bound.
Dehgardi, N., Chellali, M. (2021). Outer independent Roman domination number of trees. Communications in Combinatorics and Optimization, 6(2), 273-286. doi: 10.22049/cco.2021.27072.1191
MLA
Nasrin Dehgardi; M Chellali. "Outer independent Roman domination number of trees". Communications in Combinatorics and Optimization, 6, 2, 2021, 273-286. doi: 10.22049/cco.2021.27072.1191
HARVARD
Dehgardi, N., Chellali, M. (2021). 'Outer independent Roman domination number of trees', Communications in Combinatorics and Optimization, 6(2), pp. 273-286. doi: 10.22049/cco.2021.27072.1191
VANCOUVER
Dehgardi, N., Chellali, M. Outer independent Roman domination number of trees. Communications in Combinatorics and Optimization, 2021; 6(2): 273-286. doi: 10.22049/cco.2021.27072.1191
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