论文标题
故障的分数匹配汉密尔顿图
Fractional matching preclusion of fault Hamiltonian graphs
论文作者
论文摘要
在互连网络中边缘故障的情况下，匹配是衡量鲁棒性的度量。作为匹配排除的概括，图的分数匹配排除数（简称为fmp的数字）是边缘的最小数量的删除数量，其删除导致没有分数完美匹配的图形，并且图形的最小匹配率是最小的fr fr fr fr fr fr fr fr freft freft and prestion fre。如果在$ g-f $中存在$ f $ g-f $的$ f $ g $，则对于任何套装$ f $ f $ f $ f $ | f | f | \ leq f $。在本文中，我们建立了$（δ-2）$ - 故障汉密尔顿图的FMP编号和FSMP数，最低度$δ\ geq 3 $。作为应用程序，确定了一些知名网络的FMP号和FSMP数。
Matching preclusion is a measure of robustness in the event of edge failure in interconnection networks. As a generalization of matching preclusion, the fractional matching preclusion number (FMP number for short) of a graph is the minimum number of edges whose deletion results in a graph that has no fractional perfect matchings, and the fractional strong matching preclusion number (FSMP number for short) of a graph is the minimum number of edges and/or vertices whose deletion leaves a resulting graph with no fractional perfect matchings. A graph $G$ is said to be $f$-fault Hamiltonian if there exists a Hamiltonian cycle in $G-F$ for any set $F$ of vertices and/or edges with $|F|\leq f$. In this paper, we establish the FMP number and FSMP number of $(δ-2)$-fault Hamiltonian graphs with minimum degree $δ\geq 3$. As applications, the FMP number and FSMP number of some well-known networks are determined.
