探索对奇边优美差全着色封闭的图格  

Graphic Lattices Having the Closeness of W-type Colorings

作　　者：张明军 杨见青 姚兵 ZHANG Mingjun;YANG Jianqing;YAO Bing(School of Information Engineering and Artificial Intelligence,Lanzhou University of Finance and Economics,Lanzhou 730020;Key Laboratory of E-Business Technology and Application of Gansu Province,Lanzhou 730020;College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070)

机构地区：[1]兰州财经大学信息工程与人工智能学院,兰州730020 [2]甘肃省电子商务技术与应用重点实验室,兰州730020 [3]西北师范大学数学与统计学院,兰州730070

出　　处：《工程数学学报》2024年第2期311-325,共15页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(61662066);兰州财经大学高等教育研究项目(LJZ202309);兰州财经大学科研资助项目(Lzufe2022B-002);兰州财经大学中国西北金融研究中心项目(JYYZ201905).

摘　　要：为深入拓扑编码的研究,定义了新的图全标号和图全着色:(集有序)奇边优美差全标号/全着色,孪生(集有序)奇边优美差全标号/全着色。证明了若偶图T承认集有序奇优美标号,则给偶图T添加m片叶子后得到的偶图T∗承认一个奇边优美差全着色;每棵树承认一个奇边优美差全着色。定理的证明均可转化为可行、有效的算法。为建立随机着色的图格,给出随机添加叶子的奇边优美差全着色算法和一致-k∗优美差算法,建立了对奇边优美差全着色封闭的一致-k∗优美差图格、孪生一致-(k∗,n∗)优美差图格,以及一个图格同态到另一个图格的图格同态。For deeply investigating topological coding,we define new graph total labelings/total colorings:(set-ordered)odd-edge graceful-difference total labelings/total colorings,twin(set-ordered)odd-edge graceful-difference total labelings/total colorings.We prove two results as follows:If bipartite graph T admits a set-ordered odd-graceful labeling,then the bipartite graph T∗obtained by adding m leaves to T admits an odd-edge graceful-difference total coloring;Each tree admits an odd-edge graceful-difference total coloring.For building randomly graph lattices,we present the algorithm of odd-edge graceful-difference total coloring based on adding randomly leaves and the uniformly k∗graceful-difference algorithm,and make uniformly k∗graceful-difference graph lattices,twin uniformly(k∗,n∗)graceful-difference graph lattices,as well as a graphic lattice is homomorphism to another graphic lattice,called graphic-lattice homomorphism.

关 键 词：格密码 拓扑编码 奇边优美差全着色 图格 非对称密码学 

分 类 号：O157.5[理学—数学]