A plane matching is a

plane graph consisting of pairwise disjoint edges.

Every

plane graph has a dual graph , formed by assigning a vertex of , to each face of and joining two vertices of by edges if and only if the corresponding faces of share edges in their boundaries.

If G is a

plane graph and x, y [member of] V (G), then the dual distance of x and y is equal to the minimum number of crossings of G with a closed curve in the plane joining x and y.

The set of [alpha]-orientations of a

plane graph has a natural distributive lattice structure.

If we assign labels from the set 1, 2, 3,, V (G) E(G) F (G) to the vertices, edges and faces of

plane graph G in such a way that each vertex, edge and face receives exactly one label and each number is used exactly once as a label such a labeling is called magic labeling of type (1, 1, 1).

Suppose G is a finite

plane graph with vertex set V(G) and edge set E(G).

Theorem 5 ([3], Euler's formula) In a connected

plane graph G with n vertices, e edges and f faces (regions), n - [epsilon] + f = 2.

In the following, V (G), A(G), and F(G) denote respectively the sets of vertices, edges/arcs, and faces of a

plane graph G.

Research on this paper was initiated at the Workshop on Counting and Enumerating of

Plane Graphs held in March 2013 at Schloss Dagstuhl.

Semanicova- Fenovcikova, Super d-antimagic labelings of disconnected

plane graphs, Acta Math.

diameter) of

plane graphs, edge-transitive graphs and general (bipartite) graphs.

Semanicov'a-Fenovc'ikov'a, Super magic and antimagic labelings of disjoint union of

plane graphs, Science Int.