首页|探索对奇边优美差全着色封闭的图格

探索对奇边优美差全着色封闭的图格

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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.
Graphic Lattices Having the Closeness of W-type Colorings
For deeply investigating topological coding,we define new graph total label-ings/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 color-ing 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.

lattice-based cryptographytopological codingodd-edge graceful-difference total coloringgraphic latticeasymmetric cryptography

张明军、杨见青、姚兵

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兰州财经大学信息工程与人工智能学院,兰州 730020

甘肃省电子商务技术与应用重点实验室,兰州 730020

西北师范大学数学与统计学院,兰州 730070

格密码 拓扑编码 奇边优美差全着色 图格 非对称密码学

国家自然科学基金兰州财经大学高等教育研究项目兰州财经大学科研项目兰州财经大学中国西北金融研究中心项目

61662066LJZ202309Lzufe2022B-002JYYZ201905

2024

工程数学学报
西安交通大学

工程数学学报

CSTPCD北大核心
影响因子:0.302
ISSN:1005-3085
年,卷(期):2024.41(2)
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