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 (, 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
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.