A nonorientable triangular embedding of Kn − K2, n ≡ 8 (mod 12)

Triangular Cayley maps of Kn, n, n

Regular hamiltonian embeddings of Kn, n and regular triangular embeddings of Kn, n, n

We give a group-theoretic proof of the following fact, proved initially by methods of topological design theory: Up to isomorphism, the number of regular hamiltonian embeddings of Kn,n is 2 or 1, depending on whether n is a multiple of 8 or not. We also show that for each n there is, up to isomorphism, a unique regular triangular embedding of Kn,n,n. This is a preprint of an article accepted fo...

Mod sum graph labelling of Hm, n and Kn

The mod sum number p( G) of a connected graph G is the minimum number of isolated vertices required to transform G into a mod sum graph. It is known that the mod sum number is greater than zero for wheels, Wn, when n > 4 and for the complete graphs, Kn when n 2: 2. In this paper we show that p( Hm,n) > 0 for n > m ;::: 3. Vie show further that P(K2) = P(K3) = 1 while p(Kn) = n for n ;::: 4. We ...

Quadrangular embeddings of complete graphs∗

Hartsfield and Ringel proved that a complete graph Kn has an orientable quadrangular embedding if n ≡ 5 (mod 8), and has a nonorientable quadrangular embedding if n ≥ 9 and n ≡ 1 (mod 4). We complete the characterization of complete graphs admitting quadrangular embeddings by showing that Kn has an orientable quadrilateral embedding if n ≡ 0 (mod 8), and has a nonorientable quadrilateral embedd...

Classification of nonorientable regular embeddings of complete bipartite graphs

A 2-cell embedding of a graph G into a closed (orientable or nonorientable) surface is called regular if its automorphism group acts regularly on the flags mutually incident vertex-edge-face triples. In this paper, we classify the regular embeddings of complete bipartite graphs Kn,n into nonorientable surfaces. Such a regular embedding of Kn,n exists only when n = 2p a1 1 p a2 2 · · · p ak k (a...