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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Published in | Information sciences Vol. 108; no. 1; pp. 5 - 12 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
01.07.1998
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Subjects | |
Online Access | Get full text |
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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. |
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Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 0020-0255 1872-6291 |
DOI: | 10.1016/S0020-0255(98)10063-4 |