Geodesic visibility in graphs

Two nodes in a pebbled graph are said to be mutually visible if there exists a shortest path (a “geodesic”) between them which is unpebbled. In an earlier paper we studied this concept for node-pebbled graphs, and characterized various types of pebbled graphs that are geodesically “convex”, i.e., an...

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Bibliographic Details
Published inInformation sciences Vol. 108; no. 1; pp. 5 - 12
Main Authors Wu, Angela Y., Rosenfeld, Azriel
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.07.1998
Subjects
Geodesics
Graphs
Guarding sets
Visibility
Graphs
Visibility
Geodesics
Guarding sets
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Summary:Two nodes in a pebbled graph are said to be mutually visible if there exists a shortest path (a “geodesic”) between them which is unpebbled. In an earlier paper we studied this concept for node-pebbled graphs, and characterized various types of pebbled graphs that are geodesically “convex”, i.e., any two of their unpebbled nodes are mutually visible. In this paper we consider arc pebblings as well as node pebblings. We show that the visibility relations defined by arc and node pebblings are incomparable, and we give general characterizations of the visibility relations that can be defined by the two types of pebblings. We also show that in any arc-pebbled (node-pebbled) graph having n nodes, there exists a set of at most n/2 ( n/3 + 1) nodes from which every (unpebbled) node is visible.
Bibliography:ObjectType-Article-2
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ISSN:0020-0255
1872-6291
DOI:10.1016/S0020-0255(98)10063-4