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A characterization of graphs G with G ≈ K2(G)

✍ Scribed by Chai-Ling Deng; Chong-Keang Lim

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
311 KB
Volume
151
Category
Article
ISSN
0012-365X

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✦ Synopsis

A graph G is called a D-graph if for every set of cliques of G whose pairwise intersections are nonempty there is a vertex of G common to all the cliques of the set. A D-graph G is called a Dl-graph if it has the T 1 property: for any two distinct vertices x and y of G, there exist cliques C and D of G such that x ~ C but y¢ C and yeD but xcD.

Lim proved that if G is a Dl-graph, then G ~ K2(G). Motivated by this result of Lim, we ask the following question:

Can one characterize those graphs G with G ~ KS(G)?

In this paper, we prove that in the class of D-graphs, G ~ KS(G) if and only if G has the T1 property.

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