Name
Abstract | ||
|---|---|---|
For a graph \(G=(V,E)\), a Roman dominating function \(f:V\rightarrow \{0,1,2\}\) has the property that every vertex \(v\in V\) with \(f(v)=0\) has a neighbor \(u\) with \(f(u)=2\). The weight of a Roman dominating function \(f\) is the sum \(f(V)=\sum \nolimits _{v\in V}f(v)\), 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. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1007/s00373-015-1566-x | Graphs and Combinatorics |
Keywords | DocType | Volume |
Roman domination, Roman independence, Roman irredundance, Roman parameters | Journal | 32 |
Issue | ISSN | Citations |
1 | 1435-5914 | 1 |
PageRank | References | Authors |
0.35 | 4 | 5 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mustapha Chellali | 1 | 188 | 38.24 |
| Teresa W. Haynes | 2 | 774 | 94.22 |
| Sandra Mitchell Hedetniemi | 3 | 709 | 122.94 |
| Stephen T. Hedetniemi | 4 | 1575 | 289.01 |
| Alice A. McRae | 5 | 163 | 21.29 |