The non-orientable genus of some metacyclic groups

  title={The non-orientable genus of some metacyclic groups},
  author={Toma{\vz} Pisanski and Thomas W. Tucker and Dave Witte Morris},
AbstractWe describe non-orientable, octagonal embeddings for certain 4-valent, bipartite Cayley graphs of finite metacyclic groups, and give a class of examples for which this embedding realizes the non-orientable genus of the group. This yields a construction of Cayley graphs for which $$2\gamma - \tilde \gamma $$ is arbitrarily large, where γ and $$\tilde \gamma $$ are the orientable genus and the non-orientable genus of the Cayley graph. 


A process is provided for conducting organic compound conversion over a catalyst comprising a zeolite composition prepared by a method which comprises compositing a specific zeolite material with



On the genus of the semidirect product of ℤ9 by ℤ3

We show that the non-commutative semidirect product Γ of ℤ9 by ℤ3 has orientable genus 4. In other words, some Cayley graph of Γ embeds in an orientable surface of genus 4 (Euler characteristic −6),

Generators and relations for discrete groups

1. Cyclic, Dicyclic and Metacyclic Groups.- 2. Systematic Enumeration of Cosets.- 3. Graphs, Maps and Cayley Diagrams.- 4. Abstract Crystallography.- 5. Hyperbolic Tessellations and Fundamental

A determination of the toroidal k-metacyclic groups

This paper develops a methodology for using Proulx's classification of toroidal groups by presentation to determine whether an explicitly given group is toroidal.

Graphs, Groups and Surfaces

Historical Setting. A Brief Introduction to Graph Theory. The Automorphism Group of a Graph. The Cayley Color Graph of a Group Presentation. An Introduction to Surface Topology. Imbedding Problems in

Generalized Embedding Schemes

  • S. Stahl
  • Mathematics, Computer Science
    J. Graph Theory
  • 1978
Covering projections are used to provide a logical foundation for the generalized embedding schemes which describe embeddings of graphs on closed surfaces that are not necessarily orientable.

Theory of Groups of Finite Order

  • G. M.
  • Mathematics
  • 1911
IN the new edition of Prof. Burnside's standard work important changes have been made by rearrangement of old material, and by addition of new. The main feature, for which many English readers will

YOUNGS : The imbedding of graphs in manifolds

  • J . Math . Mech .
  • 1963

LOMONACO : A determination of the toroidal Kmetacyclic groups

  • Theory of Groups of Finite Order

On the genus of the semidirect product of Z Q by z 3

  • J . Graph Theory
  • 1989