On calculating connected dominating set for efficient routing in ad hoc wireless networks
DIALM '99 Proceedings of the 3rd international workshop on Discrete algorithms and methods for mobile computing and communications
Connected Domination and Spanning Trees with Many Leaves
SIAM Journal on Discrete Mathematics
Domination in planar graphs with small diameter
Journal of Graph Theory
Construction of strongly connected dominating sets in asymmetric multihop wireless networks
Theoretical Computer Science
Connected Domination Number of a Graph and its Complement
Graphs and Combinatorics
Note: On graphs for which the connected domination number is at most the total domination number
Discrete Applied Mathematics
| Hi-index | 0.04 |
A subset S of vertices in a graph G=(V,E) is a connected dominating set of G if every vertex of V@?S is adjacent to a vertex in S and the subgraph induced by S is connected. The minimum cardinality of a connected dominating set of G is the connected domination number @c"c(G). The girth g(G) is the length of a shortest cycle in G. We show that if G is a connected graph that contains at least one cycle, then @c"c(G)=g(G)-2, and we characterize the graphs obtaining equality in this bound. We also establish various upper bounds on the connected domination number of a graph, as well as Nordhaus-Gaddum type results.