Closed 2-cell Embeddings of 5-crosscap Embeddable Graphs

Closed 2-cell embeddings of 4 cross-cap embeddable graphs

The strong embedding conjecture states that every 2-connected graph has a closed 2-cell embedding in some surface , i . e . an embedding that each face is bounded by a circuit in the graph . A graph is called k -crosscap embeddable if it can be embedded in the surface of non-orientable genus k . We confirm the strong embedding conjecture for 5-crosscap embeddable graphs . As a corollary , every...

Closed 2-cell embeddings of graphs with no V8-minors

A closed 2-cell embedding of a graph embedded in some surface is an embedding such that each face is bounded by a cycle in the graph. The strong embedding conjecture says that every 2-connected graph has a closed 2-cell embedding in some surface. In this paper, we prove that any 2-connected graph without V8 (the M obius 4-ladder) as a minor has a closed 2-cell embedding in some surface. As a c...

Labeling Subgraph Embeddings and Cordiality of Graphs

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, a vertex labeling $f : V(G)rightarrow mathbb{Z}_2$ induces an edge labeling $ f^{+} : E(G)rightarrow mathbb{Z}_2$ defined by $f^{+}(xy) = f(x) + f(y)$, for each edge $ xyin E(G)$.  For each $i in mathbb{Z}_2$, let $ v_{f}(i)=|{u in V(G) : f(u) = i}|$ and $e_{f^+}(i)=|{xyin E(G) : f^{+}(xy) = i}|$. A vertex labeling $f$ of a graph $G...

On cyclically embeddable graphs

An embedding of a simple graph G into its complement G is a permutation σ on V (G) such that if an edge xy belongs to E(G), then σ(x)σ(y) does not belong to E(G). In this note we consider some families of embeddable graphs such that the corresponding permutation is cyclic.

Polynomial Invariants of Embeddings of Graphs on Closed Surfaces