Open Journal of Discrete Mathematics

Volume 7, Issue 2 (April 2017)

ISSN Print: 2161-7635   ISSN Online: 2161-7643

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Competition Numbers of Several Kinds of Triangulations of a Sphere

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DOI: 10.4236/ojdm.2017.72006    1,010 Downloads   1,363 Views  Citations

ABSTRACT

It is hard to compute the competition number for a graph in general and characterizing a graph by its competition number has been one of important research problems in the study of competition graphs. Sano pointed out that it would be interesting to compute the competition numbers of some triangulations of a sphere as he got the exact value of the competition numbers of regular polyhedra. In this paper, we study the competition numbers of several kinds of triangulations of a sphere, and get the exact values of the competition numbers of a 24-hedron obtained from a hexahedron by adding a vertex in each face of the hexahedron and joining the vertex added in a face with the four vertices of the face, a class of dodecahedra constructed from a hexahedron by adding a diagonal in each face of the hexahedron, and a triangulation of a sphere with 3n (n≥2) vertices.

Share and Cite:

Zhao, Y. , Fang, Z. , Cui, Y. , Ye, G. and Cao, Z. (2017) Competition Numbers of Several Kinds of Triangulations of a Sphere. Open Journal of Discrete Mathematics, 7, 54-64. doi: 10.4236/ojdm.2017.72006.

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