On the homotopy type of the clique graph

Journal of the Brazilian Computer Society

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