Topic
Pappus graph
About: Pappus graph is a research topic. Over the lifetime, 14 publications have been published within this topic receiving 89 citations.
Papers
TL;DR: All pairwise non-isomorphic p-elementary abelian covering projections admitting a lift of an arc-transitive subgroup of the full automorphism group of the Pappus graph F"1"8, the unique connected cubic symmetric graph of order 18, are constructed.
24 citations
TL;DR: Several new constructions for small generalized polygons using small projective planes together with a conic or a unital, using other small polygons, and using certain graphs such as the Coxeter graph and the Pappus graph are presented.
14 citations
TL;DR: It is found that certain distance-regular graphs must contain Pappus subgraphs and, as a corollary, the existence of the last bipartite distance- regular graph of diameter 6 is ruled out.
Abstract: We find that certain distance-regular graphs must contain Pappus subgraphs and, as a corollary, are able to rule out the existence of the last bipartite distance-regular graph of diameter 6 in the tables of [2] for which the existence was still undecided.
9 citations
TL;DR: An infinite family of non-Cayley cubic $2-regular graphs of type $2^2$ with a solvable automorphism group is constructed and the smallest graph in this family has order 6174.
5 citations
TL;DR: In this paper, irreducible pseudo 2-factor isomorphic cubic bipartite graphs are characterized proving that the only Pseudo 2-Factor isomorphic irReducible Levi graphs are the Heawood and Pappus graphs.
Abstract: A bipartite graph is pseudo 2-factor isomorphic if the number of circuits in each 2-factor of the graph is always even or always odd. We proved (Abreu et al., J Comb Theory B 98:432---442, 2008) that the only essentially 4-edge-connected pseudo 2-factor isomorphic cubic bipartite graph of girth 4 is K 3,3, and conjectured (Abreu et al., 2008, Conjecture 3.6) that the only essentially 4-edge-connected cubic bipartite graphs are K 3,3, the Heawood graph and the Pappus graph. There exists a characterization of symmetric configurations n 3 due to Martinetti (1886) in which all symmetric configurations n 3 can be obtained from an infinite set of so called irreducible configurations (Martinetti, Annali di Matematica Pura ed Applicata II 15:1---26, 1888). The list of irreducible configurations has been completed by Boben (Discret Math 307:331---344, 2007) in terms of their irreducible Levi graphs. In this paper we characterize irreducible pseudo 2-factor isomorphic cubic bipartite graphs proving that the only pseudo 2-factor isomorphic irreducible Levi graphs are the Heawood and Pappus graphs. Moreover, the obtained characterization allows us to partially prove the above Conjecture.
4 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2020 | 1 |
| 2017 | 2 |
| 2014 | 1 |
| 2012 | 1 |
| 2011 | 1 |
| 2010 | 1 |