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Lattice theory has been believed to resist classical computers and quantum computers. Since there are connections between traditional lattices and graphic lattices, it is meaningful to research graphic lattices. We define the so-called ice-flower systems by our uncolored or colored leaf-splitting and leaf-coinciding operations. These ice-flower systems enable us to construct several star-graphic lattices. We use our star-graphic lattices to express some well-known results of graph theory and compute the number of elements of a particular star-graphic lattice. For more researching ice-flower systems and star-graphic lattices we propose Decomposition Number String Problem, finding strongly colored uniform ice-flower systems and connecting our star-graphic lattices with traditional lattices.
Lattice-based cryptography is not only for thwarting future quantum computers, and is also the basis of Fully Homomorphic Encryption. Motivated from the advantage of graph homomorphisms we combine graph homomorphisms with graph total colorings togeth
Lattice-based Cryptography is considered to have the characteristics of classical computers and quantum attack resistance. We will design various graphic lattices and matrix lattices based on knowledge of graph theory and topological coding, since ma
A {em connectivity function} on a set $E$ is a function $lambda:2^Erightarrow mathbb R$ such that $lambda(emptyset)=0$, that $lambda(X)=lambda(E-X)$ for all $Xsubseteq E$, and that $lambda(Xcap Y)+lambda(Xcup Y)leq lambda(X)+lambda(Y)$ for all $X,Y s
The class of quasi-graphic matroids recently introduced by Geelen, Gerards, and Whittle generalises each of the classes of frame matroids and lifted-graphic matroids introduced earlier by Zaslavsky. For each biased graph $(G, mathcal B)$ Zaslavsky de
For an abelian group $Gamma$, a $Gamma$-labelled graph is a graph whose vertices are labelled by elements of $Gamma$. We prove that a certain collection of edge sets of a $Gamma$-labelled graph forms a delta-matroid, which we call a $Gamma$-graphic d