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Article overview
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Graph Set-colorings And Hypergraphs In Topological Coding | | Bing Yao
; Fei Ma
; | | Date: |
31 Jan 2022 | | Abstract: | In order to make more complex number-based strings from topological coding
for defending against the intelligent attacks equipped with quantum computing
and providing effective protection technology for the age of quantum computing,
we will introduce set-colored graphs admitting set-colorings that has been
considerable cryptanalytic significance, and especially related with
hypergraphs. We use the set-coloring of graphs to reflect the intersection of
elements, and add other constraint requirements to express more connections
between sets (as hyperedges). Since we try to find some easy and effective
techniques based on graph theory for practical application, we use
intersected-graphs admitting set-colorings defined on hyperedge sets to observe
topological structures of hypergraphs, string-type Topcode-matrix, set-type
Topcode-matrix, graph-type Topcode-matrix, hypergraph-type Topcode-matrix,
matrix-type Topcode-matrix emph{etc}. We will show that each connected graph
is the intersected-graph of some hypergraph and investigate hypergraph’s
connectivity, colorings of hypergraphs, hypergraph homomorphism, hypernetworks,
scale-free network generator, compound hypergraphs having their
intersected-graphs with vertices to be hypergraphs (for high-dimensional
extension diagram). Naturally, we get various graphic lattices, such as
edge-coincided intersected-graph lattice, vertex-coincided intersected-graph
lattice, edge-hamiltonian graphic lattice, hypergraph lattice and
intersected-network lattice. Many techniques in this article can be translated
into polynomial algorithms, since we are aiming to apply hypergraphs and graph
set-colorings to homomorphic encryption and asymmetric cryptograph. | | Source: | arXiv, 2201.13354 | | Services: | Forum | Review | PDF | Favorites | |
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