Paper Info
Title
Total Roman {3}-domination in Graphs
Abstract
For a graph G=(V,E) with vertex set V=V(G) and edge set E=E(G), a Roman {3}-dominating function (R{3}-DF) is a function f:V(G)->{0,1,2,3} having the property that n-ary sumation u is an element of NG(v)f(u)>= 3, if f(v)=0, and n-ary sumation u is an element of NG(v)f(u)>= 2, if f(v)=1 for any vertex v is an element of V(G). The weight of a Roman {3}-dominating function f is the sum f(V)= n-ary sumation v is an element of V(G)f(v) and the minimum weight of a Roman {3}-dominating function on G is the Roman {3}-domination number of G, denoted by gamma{R3}(G). Let G be a graph with no isolated vertices. The total Roman {3}-dominating function on G is an R{3}-DF f on G with the additional property that every vertex v is an element of V with f(v)not equal 0 has a neighbor w with f(w)not equal 0. The minimum weight of a total Roman {3}-dominating function on G, is called the total Roman {3}-domination number denoted by gamma t{R3}(G). We initiate the study of total Roman {3}-domination and show its relationship to other domination parameters. We present an upper bound on the total Roman {3}-domination number of a connected graph G in terms of the order of G and characterize the graphs attaining this bound. Finally, we investigate the complexity of total Roman {3}-domination for bipartite graphs.
Year
DOI
Venue
2020
10.3390/sym12020268
SYMMETRY-BASEL
Keywords
DocType
Volume
Roman domination,Roman {3}-domination,Total Roman {3}-domination
Journal
12
Issue
Citations 
PageRank 
2
0
0.34
References 
Authors
0
3
Name
Order
Citations
PageRank
Zehui Shao111930.98
D.A. Mojdeh228.19
Lutz Volkmann3943147.74