CDS in Disk-Containment Graphs

Ding-Zhu Du and Peng-Jun Wan
Additional contact information
Ding-Zhu Du: University of Texas, Dallas
Peng-Jun Wan: Illinois Institute of Technology

Chapter Chapter 8 in Connected Dominating Set: Theory and Applications, 2013, pp 133-149 from Springer

Abstract: Abstract Disk-containment graphs are generalizations of the unit disk graphs. Consider a finite planar set V of nodes. Each node v is associated with a disk of radius r v centered at v. The disk-containment graph (DCG) of V is the undirected graph $$G = \left (V,E\right )$$ in which uv ∈ E if and only if the disk-associated u contains v and disk-associated v contains u. In other words, uv ∈ E if and only if the Euclidean distance between u and v is no more than $$\min \left \{{r}_{u},{r}_{v}\right \}$$ . When all the disks associated with the nodes in V have unit radius, then the DCG of V is exactly the UDG of V. The DCG arises naturally from communication topologies of multihop wireless networks with disparate communication ranges [102, 124]. Indeed, if V represents the set of nodes in a multihop wireless network and each r v represents the communication radius of the node v, the DCG of V is exactly the symmetric communication topology of the multihop wireless network.

Keywords: Multihop Wireless Networks; Unit Disk Graph; Communication Radius; Communication Topology; Connected Domination Number (search for similar items in EconPapers)
Date: 2013
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-5242-3_8

Ordering information: This item can be ordered from
http://www.springer.com/9781461452423

DOI: 10.1007/978-1-4614-5242-3_8

Access Statistics for this chapter

More chapters in Springer Optimization and Its Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().