Keywords: A-like matrices, distance-regular graphs, HypercubesPublished in RUP: 15.10.2013; Views: 3513; Downloads: 73 Link to full text
Abstract: It is shown that every connected vertex-transitive graph of order ▫$4p$▫, where ▫$p$▫ is a prime, is hamiltonian with the exception of the Coxeter graph which is known to possess a Hamilton path.Keywords: graph theory, vertex-transitive graphs, Hamilton cycle, automorphism groupPublished in RUP: 15.10.2013; Views: 3661; Downloads: 39 Link to full text
Abstract: Let ▫$\Gamma$▫ denote a bipartite ▫$Q$▫-polynomial distance-regular graph with diameter ▫$d \ge 3$▫, valency ▫$k \ge 3$▫ and intersection number ▫$c_2=1$▫. We show that ▫$\Gamma$▫ has a certain equitable partition of its vertex set which involves ▫$4d-4$▫ cells. We use this partition to show that the intersection numbers of ▫$\Gamma$▫ satisfy the following divisibility conditions: (I) ▫$c_{i+1}-1$▫ divides ▫$c_i(c_i-1)$▫ for ▫$2 \le i \le d-1$▫, and (II) ▫$b_{i-1}-1$▫ divides ▫$b_i(b_i-1)$▫ for ▫$1 \le i \le d-1$▫. Using these divisibility conditions we show that ▫$\Gamma$▫ does not exist if ▫$d=4$▫.Keywords: mathematics, grah theory, distance-regular graphs, ▫$Q$▫-polynomial property, equitable partitionsPublished in RUP: 15.10.2013; Views: 4047; Downloads: 37 Link to full text
Keywords: arc-transitive graphs, graph-restrictive group, local actionPublished in RUP: 15.10.2013; Views: 3707; Downloads: 72 Link to full text
