Trapezoid graphs and their coloring
Discrete Applied Mathematics
Domination on cocomparability graphs
SIAM Journal on Discrete Mathematics
On the 2-chain subgraph cover and related problems
Journal of Algorithms
Dominations in trapezoid graphs
Information Processing Letters
Steiner set and connected domination in trapezoid graphs
Information Processing Letters
Trapezoid graphs and generalizations, geometry and algorithms
Discrete Applied Mathematics
Weighted domination of cocomparability graphs
Discrete Applied Mathematics
Graph classes: a survey
Connected domination and dominating clique in trapezoid graphs
Proceedings of the 5th Twente workshop on on Graphs and combinatorial optimization
Extended Dominating-Set-Based Routing in Ad Hoc Wireless Networks with Unidirectional Links
IEEE Transactions on Parallel and Distributed Systems
Dominating the complements of bounded tolerance graphs and the complements of trapezoid graphs
Discrete Applied Mathematics
Counting the number of vertex covers in a trapezoid graph
Information Processing Letters
On the k-tuple domination of generalized de Brujin and Kautz digraphs
Information Sciences: an International Journal
Finding minimum weight connected dominating set in stochastic graph based on learning automata
Information Sciences: an International Journal
Efficient algorithm for the vertex connectivity of trapezoid graphs
Information Processing Letters
On rainbow domination numbers of graphs
Information Sciences: an International Journal
Hi-index | 0.07 |
Given the trapezoid diagram, the problem of finding the minimum cardinality connected dominating set in trapezoid graphs was solved in O(m+n) time [Y.D. Liang, Steiner set and connected domination in trapezoid graphs, Inform. Process. Lett. 56 (2) (1995) 101-108]. Kohler [E. Kohler, Connected domination and dominating clique in trapezoid graphs, Discr. Appl. Math. 99 (2000) 91-110] recently improved this result to O(n) time. For the (vertex) weighted case, the problem of finding the minimum weighted connected dominating set in trapezoid graphs can be solved in O(m+nlogn) time [Anand Srinivasan, M.S. Chang, K. Madhukar, C. Pandu Rangan, Efficient algorithms for the weighted domination problems on trapezoid graphs, Manuscript, 1996]. Herein n (m) denotes the number of vertices (edges) of the trapezoid graph. In this paper, we show a different approach for the problem of finding the minimum cardinality connected dominating set in trapezoid graphs using O(n) time. For finding the minimum weighted connected dominating set, we show the problem can be solved in O(nloglogn) time.