Edge-symmetric Orientable Imbeddings of Complete Graphs

Enumerating the orientable 2-cell imbeddings of complete bipartite graphs

Orientable Step Domination of Complete r-Partite Graphs

This paper provides lower orientable k-step domination number and upper orientable k-step domination number of complete r-partite graph for 1 ≤ k ≤ 2. It also proves that the intermediate value theorem holds for the complete r-partite graphs.

extreme edge-friendly indices of complete bipartite graphs

let g=(v,e) be a simple graph. an edge labeling f:e to {0,1} induces a vertex labeling f^+:v to z_2 defined by $f^+(v)equiv sumlimits_{uvin e} f(uv)pmod{2}$ for each $v in v$, where z_2={0,1} is the additive group of order 2. for $iin{0,1}$, let e_f(i)=|f^{-1}(i)| and v_f(i)=|(f^+)^{-1}(i)|. a labeling f is called edge-friendly if $|e_f(1)-e_f(0)|le 1$. i_f(g)=v_f(1)-v_f(0) is called the edge-f...

Triangulations of orientable surfaces by complete tripartite graphs

Orientable triangular embeddings of the complete tripartite graph Kn,n,n correspond to biembeddings of Latin squares. We show that if n is prime there are at least e ln n−n(1+o(1)) nonisomorphic biembeddings of cyclic Latin squares of order n. If n = kp, where p is a large prime number, then the number of nonisomorphic biembeddings of cyclic Latin squares of order n is at least e ln p−p(1+ln . ...

The orientable genus of certain complete tripartite graphs

In 1969, White conjectured that the orientable genus of the complete tripartite graph Kl,m,n, with l ≥ m ≥ n, is ⌈ (l−2)(m+n−2) 4 ⌉ . In this talk we describe progress on this conjecture. We can show that White’s conjecture is true in the cases where (m, n), reduced modulo 4, is (0, 0), (0, 2), (1, 1), (2, 0), (2, 1), (2, 2), (2, 3) or (3, 3). We discuss similarities and differences between our...