论文标题
Zeon和IDEM-CLIFFORD超图问题的公式
Zeon and Idem-Clifford Formulations of Hypergraph Problems
论文作者
论文摘要
事实证明，Zeon代数可用于枚举图表中的结构，例如路径，步道，周期，匹配，集团和独立集。与普通图相比，每个边缘正好连接两个顶点，一个边缘（或“ hyperedge”）可以在HyperGraph中连接任何数量的顶点。在游戏理论中，超图称为简单游戏。超图已用于生物学，化学，图像处理，无线网络等方面的问题。在当前的工作中，Zeon（“ Nil-Clifford”）和“ Idem-Clifford”图理论方法被推广到超图。特别是，Zeon和Idem-Clifford方法用于枚举HyperGraphs中的路径，步道，独立集，集合和匹配。开发了一种寻找最小超毛电横向的方法，并提出了一些开放式超透明问题的Zeon公式。
Zeon algebras have proven to be useful for enumerating structures in graphs, such as paths, trails, cycles, matchings, cliques, and independent sets. In contrast to an ordinary graph, in which each edge connects exactly two vertices, an edge (or, "hyperedge") can join any number of vertices in a hypergraph. In game theory, hypergraphs are called simple games. Hypergraphs have been used for problems in biology, chemistry, image processing, wireless networks, and more. In the current work, zeon ("nil-Clifford") and "idem-Clifford" graph-theoretic methods are generalized to hypergraphs. In particular, zeon and idem-Clifford methods are used to enumerate paths, trails, independent sets, cliques, and matchings in hypergraphs. An approach for finding minimum hypergraph transversals is developed, and zeon formulations of some open hypergraph problems are presented.
