Graph theory with applications to algorithms and computer science
On n-domination, n-dependence and forbidden subgraphs
Graph theory with applications to algorithms and computer science
Dominating a Family of Graphs with Small Connected Subgraphs
Combinatorics, Probability and Computing
A general method in the theory of domination in graphs
International Journal of Computer Mathematics
On dominating sets of maximal outerplanar graphs
Discrete Applied Mathematics
Randomized algorithms and upper bounds for multiple domination in graphs and networks
Discrete Applied Mathematics
| Hi-index | 0.04 |
Let G=(V,E) be a simple graph, and let k be a positive integer. A subset D@?V is a k-dominating set of the graph G if every vertex v@?V-D is adjacent to at least k vertices of D. The k-domination number@c"k(G) is the minimum cardinality among the k-dominating sets of G. A subset D@?V is said to be a connectedk-dominating set if D is k-dominating and its induced subgraph is connected. D is called totalk-dominating if every vertex in V has at least k neighbors in D and it is a connected totalk-dominating set if, additionally, its induced subgraph is connected. The minimum cardinalities of a connected k-dominating set, a total k-dominating set, and a connected total k-dominating set are respectively denoted as @c"k^c(G), @c"k^t(G) and @c"k^c^,^t(G). In this paper, we establish different sharp bounds on the connected k-domination number @c"k^c(G), involving also the parameters @c"k(G), @c"k^t(G) and @c"k^c^,^t(G).