On Locally Gabriel Geometric Graphs

@article{Govindarajan2015OnLG,
  title={On Locally Gabriel Geometric Graphs},
  author={Sathish Govindarajan and A. Khopkar},
  journal={Graphs and Combinatorics},
  year={2015},
  volume={31},
  pages={1437-1452}
}
Let $$P$$P be a set of $$n$$n points in the plane. A geometric graph $$G$$G on $$P$$P is said to be locally Gabriel if for every edge $$(u,v)$$(u,v) in $$G$$G, the Euclidean disk with the segment joining $$u$$u and $$v$$v as diameter does not contain any points of $$P$$P that are neighbors of $$u$$u or $$v$$v in $$G$$G. 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… Expand

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Edge complexity of geometric graphs on convex independent point sets
In this paper, we focus on a generalised version of Gabriel graphs known as Locally Gabriel graphs ($LGGs$) and Unit distance graphs ($UDGs$) on convexly independent point sets. $UDGs$ are sub graphsExpand

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