Abstract
A map is singular if each edge is on the same face on a sruface (i.e., those have only one face on a surface). Because any map with loop is not colorable, all maps here are assumed to be loopless. In this paper povides the explicit expression of chromatic sum functions for rooted singular maps on the projective plane, the torus and the Klein bottle. From the explicit expression of chromatic sum functions of such maps, the explicit expression of enum erating functions of such maps are also derived.
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Supported by NNSFC under Grant No.10271048 and 19831080.
Zhaoxiang Li received his MS from Changsha Railway University and Ph. D from Northern Jiaotong University. His research interests cover combinatorial maps and operations research.
Yanpei Liu, Professor and Ph. D. Advisor, Graduated from University of Science and Technology of China. His interests cover combinatorial equations, topological graph theory and operations research.
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Li, Z., Liu, Y. Chromatic sums of singular maps on some surfaces. JAMC 15, 159–172 (2004). https://doi.org/10.1007/BF02935752
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DOI: https://doi.org/10.1007/BF02935752