Langford sequences and a product of digraphs

Skolem and Langford sequences and their many generalizations have applications in numerous areas. The $\otimes_h$-product is a generalization of the direct product of digraphs. In this paper we use the $\otimes_h$-product and super edge-magic digraphs to construct an exponential number of Langford sequences with certain order and defect. We also apply this procedure to extended Skolem sequences.Comment: 10 pages, 6 figures, to appear in European Journal of Combinatoric

Strings And Colorings Of Topological Coding Towards Asymmetric Topology Cryptography

We, for anti-quantum computing, will discuss various number-based strings, such as number-based super-strings, parameterized strings, set-based strings, graph-based strings, integer-partitioned and integer-decomposed strings, Hanzi-based strings, as well as algebraic operations based on number-based strings. Moreover, we introduce number-based string-colorings, magic-constraint colorings, and vector-colorings and set-colorings related with strings. For the technique of encrypting the entire network at once, we propose graphic lattices related with number-based strings, Hanzi-graphic lattices, string groups, all-tree-graphic lattices. We study some topics of asymmetric topology cryptography, such as topological signatures, Key-pair graphs, Key-pair strings, one-encryption one-time and self-certification algorithms. Part of topological techniques and algorithms introduced here are closely related with NP-complete problems or NP-hard problems.Comment: Asymmetric topology encryption is a new topic of topological coding towards the certificateless public key cryptograph