A new family of expansive graphs
Author
Abstract
An affine graph is a pair (G, ) where G is a graph and is an automorphism assigning to each vertex of G one of its neighbors. On
one hand, we obtain a structural decomposition of any affine graph (G, ) in terms of the orbits of . On the other hand, we establish
a relation between certain colorings of a graph G and the intersection graph of its cliques K(G). By using the results we construct
new examples of expansive graphs. The expansive graphs were introduced by Neumann-Lara in 1981 as a stronger notion of the
K-divergent graphs. A graph G is K-divergent if the sequence |V (Kn(G))| tends to infinity with n, where Kn+1(G) is defined by
Kn+1(G)=K(Kn(G)) for n 1. In particular, our constructions show that for any k 2, the complement of the Cartesian product
Ck, where C is the cycle of length 2k +1, is K-divergent.
Patrocinador
Partially supported by FONDAP on applied Mathematics, Fondecyt 1010442, Iniciativa Científica Milenio ICM P01-005 and CNPq under
PROSUL project Proc. 490333/2004-4.
Quote Item
DISCRETE APPLIED MATHEMATICS, Volume: 156, Issue: 7, Pages: 1125-1131, 2008
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