Nonisomorphic Orientable Quadrangular Embeddings and Edge-Colorings of K_(12s+9)  

K_(12s+9)的不同构可定向四边形嵌入及染色

作　　者：LI Zhaoxiang LIU Jiahong 李赵祥;刘家宏(中央民族大学理学院,北京100081;火箭军工程大学基础部,陕西西安710025)

机构地区：[1]College of Science,Minzu University of China,Beijing 100081,China [2]Department of Basic Courses,Rocket Force University of Engineering,Xi'an 710025,Shaanxi,China

出　　处：《Wuhan University Journal of Natural Sciences》2024年第6期563-571,共9页武汉大学学报(自然科学英文版)

摘　　要：In this paper,by constructing the current graph of the complete graph K_(12s+9)and a mapping function,we prove that K_(12s+9)(s is an odd number)has at least 6^(2s)×3^(s+3/2) nonisomorphic orientable quadrangular embeddings,and the orientable genus is(12s+9)(12s+4)/8+1.Every one of the nonisomorphic orientable quadrangular embeddings has at least twenty-four 4-edge-colors,and each color appears around each face of orientable quadrangular embeddings.本文通过构造完全图K12s+9的电流图和一个同构映射,证明了K_(12s+9)(s是一个奇数)至少有6^(2s)×3^(s+3/2)个不同构可定向四边形嵌入,且可定向亏格为(12s+9)(12s+4)/8+1.每一个不同构可定向四边形嵌入至少有24个4边染色,每种颜色出现在四边形嵌入的每一个面上。

关 键 词：quadrangular embedding maximum genus embedding edge-colorings complete graph current graph 

分 类 号：O157.5[理学—数学]