Distances and diameters on iterated clique graphs
نویسندگان
چکیده
منابع مشابه
Dismantlings and iterated clique graphs
Given a graph G and two vertices x, y ∈ V (G), we say that x is dominated by y if the closed neighbourhood of x is contained in that of y. Here we prove that if x is a dominated vertex, then G and G− {x} have the same dynamical behaviour under the iteration of the clique operator.
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Iterated clique graphs arise when the clique operator is applied to a graph more than once. Determining whether a graph is a clique graph or an iterated clique graph is usually a difficult task. The fact that being a clique graph and being an iterated clique graph are not equivalent things has been proved recently. However, it is still unknown whether the classes of second iterated clique graph...
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The clique graph K(G) of a graph G is the intersection graph of all its (maximal) cliques. A graph G is said to be K-divergent if the sequence of orders of its iterated clique graphs |Kn(G)| tends to infinity with n, otherwise it is K-convergent. K-divergence is not known to be computable and there is even a graph on 8 vertices whose K-behaviour is unknown. It has been shown that a regular Whit...
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The clique graph K(G) of a graph G is the intersection graph of all its (maximal) cliques. We explore the effect of operations like edge contraction, edge removal and others on the dynamical behaviour of a graph under the iteration of the clique operator K. As a consequence of this study, we can now prove the clique divergence of graphs for which no previously known technique would yield the re...
متن کاملDiameters and Clique Numbers of Quasi-random Graphs
We show that every quasi-random graph G(n) with n vertices and minimum degree (1 + o(1))n/2 has diameter either 2 or 3 and that every quasi-random graph G(n) with n vertices has a clique number of o(n) with wide spread.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2004
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(03)00379-2