论文标题
图和周期的超级连接的直接乘积
Super connected direct product of graphs and cycles
论文作者
论文摘要
互连网络的拓扑可以通过图$ g =（v（g），e（g））$建模。图$ g $的连接性是衡量相应网络可靠性的参数。直接产品是一种重要的图形产品。本文主要关注图和周期的直接乘积的超级连接性。 $ g $的连接性，用$κ（g）$表示，是最小顶点套装$ s \ subseteq v（g）$的大小，因此$ g-s $未连接或只有一个顶点。图$ g $据说是超级连接的，如果每个最小顶点切割都是顶点的邻居，则只需超级$κ$。由$ g \ times h $表示的两个图$ g $和$ h $的直接乘积是带有顶点set $ v（g \ times h）= v（g）\ times v（h）$和edge set $ e（g \ times h）= \ \ {（u__ _ {1}，v_ {1}，v_ {1}）{2 {2} 2 {2} {2} { u_ {1} u_ {2} \ in E（g），v_ {1} v_ {2} \ in E（h）\} $。在本文中，我们为直接产品$ g \ times c_ {n} $提供了一些足够的条件，以超级连接，其中$ c_ {n} $是$ n $ dertices上的周期。此外，最好的条件是最好的。
The topology of an interconnection network can be modeled by a graph $G=(V(G),E(G))$. The connectivity of graph $G$ is a parameter to measure the reliability of corresponding network. Direct product is one important graph product. This paper mainly focuses on the super connectedness of direct product of graphs and cycles. The connectivity of $G$, denoted by $κ(G)$, is the size of a minimum vertex set $S\subseteq V(G)$ such that $G-S$ is not connected or has only one vertex. The graph $G$ is said to be super connected, simply super-$κ$, if every minimum vertex cut is the neighborhood of a vertex with minimum degree. The direct product of two graphs $G$ and $H$, denoted by $G\times H$, is the graph with vertex set $V(G \times H) = V (G)\times V (H)$ and edge set $E(G \times H) = \{(u_{1} ,v_{1} )(u_{2} ,v_{2} )|\ u_{1}u_{2} \in E(G), v_{1}v_{2} \in E(H)\}$. In this paper, we give some sufficient conditions for direct product $G\times C_{n}$ to be super connected, where $C_{n}$ is the cycle on $n$ vertices. Furthermore, those sufficient conditions are best possible.
