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With the rapid development of quantum computing theory and quantum computer technology, the traditional public-key cryptographic algorithms face great challenges. A technology that might be able to resist attacks equipped with AI technique and quantum computers is the topological graphic password of topological coding. In order to further study topological coding, we use the multiple constraints of graph colorings and labelings to propose new techniques made by felicitous-type labelings and parameterizing felicitous-type labelings of graph theory. We show the RANDOMLY-LEAF-adding algorithm and some connections between felicitous-type labelings and parameterizing felicitous-type labelings since they can be applied to building up graphic lattices. [ABSTRACT FROM AUTHOR]

Given a graph G and a positive integer k , the Gallai–Ramsey number is defined to be the minimum number of vertices n such that any k -edge coloring of K n contains either a rainbow (all different colored) triangle or a monochromatic copy of G. In this paper, we obtain general upper and lower bounds on the Gallai–Ramsey numbers for books B m = K 2 + K m ¯ and prove the sharp values for all m ≤ 5. [ABSTRACT FROM AUTHOR]