Edge contraction and edge removal on iterated clique graphs

Authors:
M. E. FríAs-Armenta;F. LarrióN;V. Neumann-Lara;M. A. PizañA
Affiliations:
Universidad de Sonora, Depto. de Matemáticas, Blvd. Rosales y Blvd. Luis Encinas s/n, Hermosillo 83000 Sonora, Mexico;Instituto de Matemáticas, Universidad Nacional Autónoma de México, México 04510 D.F., Mexico;Instituto de Matemáticas, Universidad Nacional Autónoma de México, México 04510 D.F., Mexico;Universidad Autónoma Metropolitana, Depto.de Ingeniería Eléctrica, Av.San Rafael Atlixco 186. Col Vicentina. Del.Iztapalapa, México 09340 D.F., Mexico
Venue:
Discrete Applied Mathematics
Year:
2013

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Abstract

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 behavior 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 result. In particular, we prove that every clique divergent graph is a spanning subgraph of a clique divergent graph with diameter two.