This article aims to provide exponential lower bounds on the number of non-isomorphic $ k
$-gonal biembeddings of the complete multipartite graph into orientable surfaces. For this …

Hartsfield and Ringel constructed orientable quadrangular embeddings of the complete
graph K n for n≡ 5 (mod 8), and nonorientable ones for n≥ 9 and n≡ 1 (mod 4). These …

A quadrangular embedding of a graph in a surface Σ, also known as a quadrangulation of Σ,
is a cellular embedding in which every face is bounded by a 4-cycle. A quadrangulation of Σ …

Abstract For all $ m\geq 1$ and $ k\geq 2$, we construct closed 2-cell embeddings of the
complete graph $ K_ {8km+ 4k+ 1} $ with faces of size $4 k $ in orientable surfaces …

In this paper, by constructing the current graph of the complete graph and a mapping
function, we prove that (is an odd number) has at least nonisomorphic orientable …

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 …

We show that the number of nonisomorphic (both orientable and nonorientable) triangular
embeddings of $ K_n $, $ n\equiv 0$ or $1\pmod {3} $, $ n\geq 6$, is less than the number …

Embedding theory of graph has been widely used in very large scale integrated circuit. In
this paper, we construct the current graph and heptagonal rule of complete graphs …

This paper presents four new classes of binary quantum codes with minimum dis-tance 3
and 4, namely Class-I, Class-II, Class-III and Class-IV. The classes Class-I and Class-II are …