• Publications
  • Influence
Domination in Graphs Applied to Electric Power Networks
TLDR
The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to vertex covering and dominating set problems in graphs. Expand
  • 266
  • 41
RAINBOW DOMINATION IN GRAPHS
Assume we have a set of $k$ colors and to each vertex of a graph $G$ we assign an arbitrary subset of these colors. If we require that each vertex to which an empty set is assigned has in itsExpand
  • 117
  • 14
  • PDF
Global Defensive Alliances in Graphs
TLDR
A defensive alliance in a graph G =( V,E) is a set of vertices S V satisfying the condition that for every vertex v 2 S, the number of neighbors v has in S plus one (counting v) is at least as large as the number the neighbors it has in V S. Expand
  • 110
  • 12
  • PDF
Defending the Roman Empire--A new strategy
TLDR
This paper is supported in part by the South African National Research Foundation and the University of Natal. Expand
  • 130
  • 11
  • PDF
On Double Domination in Graphs
TLDR
We continue the study of double domination in graphs started by Harary and Haynes [5] and studied further in [1, 2, 3, 8, 9, 10]. Expand
  • 105
  • 9
  • PDF
Signed total domination in graphs
  • M. Henning
  • Computer Science, Mathematics
  • Discret. Math.
  • 6 March 2004
TLDR
We study the signed total domination number of a graph and the maximum weight of a minimal STDF on G. Expand
  • 59
  • 9
A survey of selected recent results on total domination in graphs
  • M. Henning
  • Computer Science, Mathematics
  • Discret. Math.
  • 2009
TLDR
A set S of vertices in a graph G is a total dominating set of G. Expand
  • 230
  • 8
  • PDF
A note on power domination in grid graphs
TLDR
The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well known vertex covering and dominating set problems. Expand
  • 89
  • 8
  • PDF
Signed Roman domination in graphs
TLDR
In this paper we continue the study of Roman dominating functions in graphs. Expand
  • 57
  • 7
The diameter of total domination vertex critical graphs
TLDR
We characterize the connected graphs with minimum degree one that are γ t -critical and we obtain sharp bounds on their maximum diameter. Expand
  • 52
  • 7
  • PDF
...
1
2
3
4
5
...