Doubly Even Orientable Closed 2-Cell Embeddings of the Complete Graph

Doubly Even Orientable Closed 2-cell Embeddings of the Complete Graph

For all m > 1 and k > 2, we construct closed 2-cell embeddings of the complete graph K8km+4k+1 with faces of size 4k in orientable surfaces. Moreover, we show that when k > 3 there are at least (2m − 1)!/2(2m + 1) = 22mlog2m−O(m) nonisomorphic embeddings of this type. We also show that when k = 2 there are at least 1 4π 1 2m− 5 4 ( 4m e2 ) √ m (1− o(1)) nonisomorphic embeddings of this type.

Regular Hamiltonian embeddings of the complete bipartite graph Kn,n in an orientable surface

An embedding M of a graph G is said to be regular if and only if for every two triples (v1, e1, f1) and (v2, e2, f2), where ei is an edge incident with the vertex vi and the face fi, there exists an automorphism of M which maps v1 to v2, e1 to e2 and f1 to f2. We show that for n 6≡ 0 (mod 8) there is, up to isomorphism, precisely one regular Hamiltonian embedding of Kn,n in an orientable surfac...

Orientable Hamilton Cycle Embeddings of Complete Tripartite Graphs II: Voltage Graph Constructions and Applications

In an earlier paper the authors constructed a hamilton cycle embedding of Kn,n,n in a nonorientable surface for all n ≥ 1 and then used these embeddings to determine the genus of some large families of graphs. In this two-part series, we extend those results to orientable surfaces for all n 6= 2. In part II, a voltage graph construction is presented for building embeddings of the complete tripa...

Enumerating the orientable 2-cell imbeddings of complete bipartite graphs

Complete weight enumerators of generalized doubly-even self-dual codes

For any q which is a power of 2 we describe a finite subgroup of GLqðCÞ under which the complete weight enumerators of generalized doubly-even self-dual codes over Fq are invariant. An explicit description of the invariant ring and some applications to extremality of such codes are obtained in the case q 1⁄4 4: r 2003 Elsevier Inc. All rights reserved.