Journal of the Brazilian Computer Society | |
On the homotopy type of the clique graph | |
Universidad Autónoma de México, México, MÉXICO1  Neumann-Lara, V.1  Pizaña, M. A.1  Larrión, F.1  Universidad Autónoma Metropolitana, MÉXICO1  | |
关键词: clique graphs; clique convergence; Whitney triangulations; clean triangulations; simplicial complexes; modulo 2 Betti numbers.; | |
DOI : 10.1590/S0104-65002001000200010 | |
学科分类:农业科学(综合) | |
来源: Springer U K | |
【 摘 要 】
If G is a graph, its clique graph K(G) is the intersection graph of all its (maximal) cliques. The complex G of a graph G is the simplicial complex whose simplexes are the vertex sets of the complete subgraphs of G.Here we study a sufficient condition for G and K(G) to be homotopic. Applying this result to Whitney triangulations of surfaces, we construct an infinite family of examples which solve in the affirmative Prisner's open problem 1 in Graph Dynamics (Longman, Harlow, 1995): Are there finite connected graphs G that are periodic under K and where the second modulo 2 Betti number is greater than 0?
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO201912010163821ZK.pdf | 3225KB | download |