Outer-Independent Italian Domination in Graphs

An outer-independent Italian dominating function (OIIDF) on a graph G with vertex set V(G) is defined as a function f:V(G)\rightarrow \{0,1,2\} , such that every vertex v\in V(G) with f(v)=0 has at least two neighbors assigned 1 under f or one neighbor w with f(w)=2 , and the set \{u...

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Bibliographic Details
Published in:IEEE access 2019, Vol.7, p.22756-22762
Main Authors: Fan, Wenjie, Ye, Ansheng, Miao, Fang, Shao, Zehui, Samodivkin, Vladimir, Sheikholeslami, Seyed Mahmoud
Format: Article
Language:English
Subjects:
Bipartite graph
Field-flow fractionation
Information processing
Information science
Italian domination
Mathematical functions
Minimum weight
Outer-independent Italian domination
Pattern recognition
trees
Trees (mathematics)
Upper bound
Upper bounds
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Summary:An outer-independent Italian dominating function (OIIDF) on a graph G with vertex set V(G) is defined as a function f:V(G)\rightarrow \{0,1,2\} , such that every vertex v\in V(G) with f(v)=0 has at least two neighbors assigned 1 under f or one neighbor w with f(w)=2 , and the set \{u \in V \mid f(u)=0\} is independent. The weight of an OIIDF f is the value w(f) = \sum _{u \in V(G)}f(u) . The minimum weight of an OIIDF on a graph G is called the outer-independent Italian domination number \gamma _{oiI}(G) of G . In this paper, we initiate the study of the outer-independent Italian domination number and present the bounds on the outer-independent Italian domination number in terms of the order, diameter, and vertex cover number. In addition, we establish the lower and upper bounds on \gamma _{oiI}(T) when T is a tree and characterize all extremal trees constructively. We also give the Nordhaus-Gaddum-type inequalities.
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2019.2899875