Name
Abstract | ||
|---|---|---|
A Roman dominating function (RDF) on a graph G is a function f : V(G) -> {0, 1, 2} for which every vertex assigned 0 is adjacent to a vertex assigned 2. The weight of an RDF is the value omega(f ) = Sigma(u is an element of V(G))f(u). The minimum weight of an RDF on a graph G is called the Roman domination number of G. An RDF f is called an independent Roman dominating function (IRDF) if the set {v is an element of V vertical bar f (v) >= 1} is an independent set. The minimum weight of an IRDF on a graph G is called the independent Roman domination number of G and is denoted by i(R )(G). A graph G is independent Roman domination stable if the independent Roman domination number of G does not change under removal of any vertex. A graph G is said to be independent Roman domination vertex critical or i(R)-vertex critical, if for any vertex v in G, i(R)(G - nu) < i(R)(G). In this paper, we characterize independent Roman domination stable trees and we establish upper bounds on the order of independent Roman stable graphs. Also, we investigate the properties of i(R)-vertex critical graphs. In particular, we present some families of i(R)-vertex critical graphs and we characterize i(R)-vertex critical block graphs. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1109/ACCESS.2018.2883028 | IEEE ACCESS |
Keywords | Field | DocType |
Independent Roman domination, independent Roman stable graph, independent Roman domination vertex critical graphs | Graph theory,Graph,Combinatorics,Vertex (geometry),Computer science,Upper and lower bounds,Computer network,Independent set,Omega,Minimum weight,Domination analysis | Journal |
Volume | ISSN | Citations |
6 | 2169-3536 | 0 |
PageRank | References | Authors |
0.34 | 0 | 6 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Pu Wu | 1 | 2 | 2.79 |
| Zehui Shao | 2 | 119 | 30.98 |
| Enqiang Zhu | 3 | 0 | 1.35 |
| huiqin jiang | 4 | 3 | 3.83 |
| S. Nazari-Moghaddam | 5 | 3 | 2.16 |
| Seyed Mahmoud Sheikholeslami | 6 | 54 | 28.15 |