【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。更多还原

【Abstract】 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.更多还原