论文标题
广义词典产品中的哈密顿特性
Hamiltonian properties in generalized lexicographic products
论文作者
论文摘要
两个图的词典产品$ g [h] $ $ g $和$ h $是从$ g $中获得的，通过用$ h $的副本代替每个顶点，并在与相邻顶点的任何副本之间添加所有边缘。我们还考虑了广义的词典产物，以便在相同数量的顶点上用任意图代替$ g $的每个顶点。如果$ g $是一条途径，我们提出了足够和必要的条件，以提供$ g [h] $的可追溯性和哈密顿连通性，因此我们在M. Kriesell中提高并扩展了结果，这是关于词典产品中的汉密尔顿周期的注释。
The lexicographic product $G[H]$ of two graphs $G$ and $H$ is obtained from $G$ by replacing each vertex with a copy of $H$ and adding all edges between any pair of copies corresponding to adjacent vertices of $G$. We consider also the generalized lexicographic product such that we replace each vertex of $G$ with arbitrary graph on the same number of vertices. We present sufficient and necessary conditions for traceability, hamiltonicity and hamiltonian connectivity of $G[H]$ if $G$ is a path and hence we improved and extended results in M. Kriesell, A Note on Hamiltonian Cycles in Lexicographical Products.
