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• # Artykuł - szczegóły

## Discussiones Mathematicae Graph Theory

2015 | 35 | 3 | 403-418

## On Minimal Geodetic Domination in Graphs

EN

### Abstrakty

EN
Let G be a connected graph. For two vertices u and v in G, a u-v geodesic is any shortest path joining u and v. The closed geodetic interval IG[u, v] consists of all vertices of G lying on any u-v geodesic. For S ⊆ V (G), S is a geodetic set in G if ∪u,v∈S IG[u, v] = V (G). Vertices u and v of G are neighbors if u and v are adjacent. The closed neighborhood NG[v] of vertex v consists of v and all neighbors of v. For S ⊆ V (G), S is a dominating set in G if ∪u∈S NG[u] = V (G). A geodetic dominating set in G is any geodetic set in G which is at the same time a dominating set in G. A geodetic dominating set in G is a minimal geodetic dominating set if it does not have a proper subset which is itself a geodetic dominating set in G. The maximum cardinality of a minimal geodetic dom- inating set in G is the upper geodetic domination number of G. This paper initiates the study of minimal geodetic dominating sets and upper geodetic domination numbers of connected graphs.

EN

403-418

wydano
2015-08-01
otrzymano
2013-12-28
poprawiono
2014-06-25
zaakceptowano
2014-08-01
online
2015-07-29

### Twórcy

autor
• Department of Mathematics and Statistics MSU-Iligan Institute of Technology Iligan City, Philippines
autor
• Department of Mathematics and Statistics MSU-Iligan Institute of Technology Iligan City, Philippines

### Bibliografia

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