A Roman Domination Chain

For a graph G = ( V , E ) , a Roman dominating function f : V → { 0 , 1 , 2 } has the property that every vertex v ∈ V with f ( v ) = 0 has a neighbor u with f ( u ) = 2 . The weight of a Roman dominating function f is the sum f ( V ) = ∑ v ∈ V f ( v ) , and the minimum weight of a Roman dominating...

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Bibliographic Details
Published inGraphs and combinatorics Vol. 32; no. 1; pp. 79 - 92
Main Authors Chellali, Mustapha, Haynes, Teresa W., Hedetniemi, Sandra M., Hedetniemi, Stephen T., McRae, Alice A.
Format Journal Article
LanguageEnglish
Published Tokyo Springer Japan 2016
Springer Nature B.V
Subjects
Chains
Combinatorial analysis
Combinatorics
Engineering Design
Graphs
Inequalities
Mathematical functions
Mathematics
Mathematics and Statistics
Minimum weight
Original Paper
Roman
Sharpness
Texts
Roman independence
Roman domination
Roman irredundance
Roman parameters
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Summary:For a graph G = ( V , E ) , a Roman dominating function f : V → { 0 , 1 , 2 } has the property that every vertex v ∈ V with f ( v ) = 0 has a neighbor u with f ( u ) = 2 . The weight of a Roman dominating function f is the sum f ( V ) = ∑ v ∈ V f ( v ) , and the minimum weight of a Roman dominating function on G is the Roman domination number of G . In this paper, we define the Roman independence number, the upper Roman domination number and the upper and lower Roman irredundance numbers, and then develop a Roman domination chain parallel to the well-known domination chain. We also develop sharpness, strictness and bounds for the Roman domination chain inequalities.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-015-1566-x