Concentric Bilinski diagrams
نویسندگان
چکیده
A Bilinski diagram (respectively, B∗-diagram) is a labeling of a planar map with respect to the regional distance of its vertices and faces from a central vertex (respectively, face). Such diagrams are concentric if for each k ≥ 1, the set of vertices at regional distance k from the central vertex or face induces a circuit. The class Ga,b consists of all 1-ended, 3-connected planar maps with the property that every valence is finite and at least a and every covalence is finite and at least b. A map in the subclass Ga,b+ of Ga,b contains no adjacent b-covalent faces, and dually a map in Ga+,b contains no adjacent a-valent vertices. It is shown that all Bilinski diagrams and all B∗-diagrams of all maps in G6,3, G4,4, G3,6, G5,3+ and G3+,5 are concentric.
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عنوان ژورنال:
- Australasian J. Combinatorics
دوره 30 شماره
صفحات -
تاریخ انتشار 2004