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Thankachy, Maya; Chandran, Ullas; Tuite, James; Thomas, Elias; Di Stefano, Gabriele and Erskine, Grahame
(2023).
Abstract
In this paper we generalise the notion of visibility from a point in an integer lattice to the setting of graph theory. For a vertex of a graph
, we say that a set
is an
if for any
the shortest
-paths in
contain no point of
. We investigate the largest and smallest orders of maximum
-position sets in graphs, determining these numbers for common classes of graphs and giving bounds in terms of the girth, vertex degrees, diameter and radius. Finally we discuss the complexity of finding maximum vertex position sets in graphs.
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About
- Item ORO ID
- 87516
- Item Type
- Journal Item
- ISSN
- 1234-3099
- Project Funding Details
-
Funded Project Name Project ID Funding Body EPSRC EP/W522338/1 EPSRC London Mathematical Society Early Career Fellowship ECF-2021-27 LMS - Keywords
- geodesic; vertex position set; vertex position number; general position
- Academic Unit or School
-
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM) - Related URLs
-
- https://arxiv.org/abs/2209.00359(Publication)
- Depositing User
- James Tuite