Annihilators in graphs
type: Item
instance of: scholarly article
title: Annihilators in graphs
zbMATH Open document ID: 0678.05029
DOI: 10.1007/BF03323401
author: J. Nieminen
published in: Results in Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The author introduces the annihilator \(\lceil a,b\rceil\) of an undirected graph G to be the set of all vertices reachable from a by a geodesic via b, and relates it to a similar concept for lattices. \(\lceil a,b\rceil\) is called prime if \(\lceil a,b\rceil \cap \lceil b,a\rceil =\emptyset\) and \(\lceil a,b\rceil \cup \lceil b,a\rceil\) covers all the vertices of G. G is a prime annihilator intersection graph if each annihilator is the intersection of prime annihilators. Characterizations of the class of prime annihilator graphs (a superclass of the bipartite graphs) are given, and also some applications of annihilators to center problems.
reviewed by: Christoph Schulz
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 06D99
zbMATH DE Number: 4110722
zbMATH Keywords: distance in a graph
zbMATH Keywords: geodesic
MaRDI profile type: Publication
cites work: Annihilators in modular lattices
cites work: Distance in graphs
cites work: Relative annihilators in lattices
cites work: Distance center and centroid of a median graph
full work available at URL: https://doi.org/10.1007/bf03323401
OpenAlex ID: W2141197672
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description: scientific article; zbMATH DE number 4110722