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On Locally Gabriel Geometric Graphs

Govindarajan, Sathish and Khopkar, Abhijeet (2015) On Locally Gabriel Geometric Graphs. In: GRAPHS AND COMBINATORICS, 31 (5). pp. 1437-1452.

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Official URL: http://dx.doi.org/10.1007/s00373-014-1482-5

Abstract

Let be a set of points in the plane. A geometric graph on is said to be locally Gabriel if for every edge in , the Euclidean disk with the segment joining and as diameter does not contain any points of that are neighbors of or in . A locally Gabriel graph(LGG) is a generalization of Gabriel graph and is motivated by applications in wireless networks. Unlike a Gabriel graph, there is no unique LGG on a given point set since no edge in a LGG is necessarily included or excluded. Thus the edge set of the graph can be customized to optimize certain network parameters depending on the application. The unit distance graph(UDG), introduced by Erdos, is also a LGG. In this paper, we show the following combinatorial bounds on edge complexity and independent sets of LGG: (i) For any , there exists LGG with edges. This improves upon the previous best bound of . (ii) For various subclasses of convex point sets, we show tight linear bounds on the maximum edge complexity of LGG. (iii) For any LGG on any point set, there exists an independent set of size .

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the SPRINGER JAPAN KK, CHIYODA FIRST BLDG EAST, 3-8-1 NISHI-KANDA, CHIYODA-KU, TOKYO, 101-0065, JAPAN
Keywords: Geometric proximity graphs; Gabriel graphs; Locally Gabriel graphs; Edge complexity; Convex point sets; Independent set
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Depositing User: Id for Latest eprints
Date Deposited: 24 Sep 2015 07:01
Last Modified: 24 Sep 2015 07:01
URI: http://eprints.iisc.ac.in/id/eprint/52437

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