scholarly journals Metric Dimension for Gabriel Unit Disk Graphs Is NP-Complete

2013 ◽  
pp. 90-92 ◽  
Author(s):  
Stefan Hoffmann ◽  
Egon Wanke
Keyword(s):  
Unit Disk ◽  
Metric Dimension ◽  
Unit Disk Graphs ◽  
Np Complete

ROMAN DOMINATION AND ITS VARIANTS IN UNIT DISK GRAPHS

2010 ◽  
Vol 02 (01) ◽  
pp. 99-105 ◽  
Author(s):  
WEIPING SHANG ◽  
XIUMEI WANG ◽  
XIAODONG HU
Keyword(s):  
Mathematical Model ◽  
Unit Disk ◽  
Wireless Ad Hoc Networks ◽  
Ad Hoc ◽  
Dominating Set ◽  
Roman Domination ◽  
Intersection Graphs ◽  
Unit Disk Graphs ◽  
Np Complete ◽  
Hoc Networks

Unit disk graphs are the intersection graphs of equal sized disks in the plane, they are widely used as a mathematical model for wireless ad-hoc networks and some problems in computational geometry. In this paper we first show that Roman dominating set and connected Roman dominating set problems in unit disk graphs are NP-complete, and then present two approximation algorithms for these problems.

scholarly journals Sparse hop spanners for unit disk graphs

2021 ◽  
pp. 101808
Author(s):  
Adrian Dumitrescu ◽  
Anirban Ghosh ◽  
Csaba D. Tóth
Keyword(s):  
Unit Disk ◽  
Unit Disk Graphs

scholarly journals Approximating Maximum Diameter-Bounded Subgraph in Unit Disk Graphs

2021 ◽  
Author(s):  
A. Karim Abu-Affash ◽  
Paz Carmi ◽  
Anil Maheshwari ◽  
Pat Morin ◽  
Michiel Smid ◽  
...  
Keyword(s):  
Unit Disk ◽  
Maximum Diameter ◽  
Unit Disk Graphs

Improper Colourings of Unit Disk Graphs

2005 ◽  
Vol 22 ◽  
pp. 123-128 ◽  
Author(s):  
F. Havet ◽  
R.J. Kang ◽  
J.-S. Sereni
Keyword(s):  
Unit Disk ◽  
Unit Disk Graphs

scholarly journals Local 7-coloring for planar subgraphs of unit disk graphs

2011 ◽  
Vol 412 (18) ◽  
pp. 1696-1704 ◽  
Author(s):  
J. Czyzowicz ◽  
S. Dobrev ◽  
H. González-Aguilar ◽  
R. Kralovic ◽  
E. Kranakis ◽  
...  
Keyword(s):  
Unit Disk ◽  
Unit Disk Graphs ◽  
Planar Subgraphs

Unit Disk Graphs

1991 ◽  
pp. 165-177 ◽  
Author(s):  
Brent N. Clark ◽  
Charles J. Colbourn ◽  
David S. Johnson
Keyword(s):  
Unit Disk ◽  
Unit Disk Graphs
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