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On Minimal Geodetic Domination in Graphs

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Nuenay H. M., Jamil F. P.

Discussiones Mathematicae Graph Theory

2015

tom 35

nr 3

403-418

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.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Jamil F. P.

1 Nuenay H. M.

1 2015

Wyniki wyszukiwania

On Minimal Geodetic Domination in Graphs