Let Γ be a regular graph with n vertices, diameter D, and d + 1 In a previous paper, the authors showed that if P (λ) > n -1, then D ≤ d -1, where P is the polynomial of degree d-1 which takes alternating values ±1 at λ 1 , . . . , λ d . The graphs satisfying P (λ) = n -1, called boundary graphs, h
Graphs obtained from Moufang loops and regular maps
✍ Scribed by T.S. Griggs; J. Širáň; R.B. Richter
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 120 KB
- Volume
- 70
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
Using ideas from regular maps, we prove the existence of infinitely many non‐vertex‐transitive Cayley graphs obtained from Moufang loops. Copyright © 2011 Wiley Periodicals, Inc. J Graph Theory
📜 SIMILAR VOLUMES
In the paper is developed a common generalization of two methods of construction of regular maps on surfaces. The first one produces graph covering projections that extend to coverings of regular embeddings of the graphs involved. The second method employs a double covering projection of graphs whic
Let c k be the smallest number of vertices in a regular graph with valency k and girth 8. It is known that c k+1 ≥ 2(1+k+k 2 +k 3 ) with equality if and only if there exists a finite generalized quadrangle of order k. No such quadrangle is known when k is not a prime power. In this case, small regul
## Abstract We prove that all 3‐connected 4‐regular planar graphs can be generated from the Octahedron Graph, using three operations. We generated these graphs up to 15 vertices inclusive. Moreover, by including a fourth operation we obtain an alternative to a procedure by Lehel to generate all con
## Abstract It has been communicated by P. Manca in this journal that all 4‐regular connected planar graphs can be generated from the graph of the octahedron using simple planar graph operations. We point out an error in the generating procedure and correct it by including an additional operation.