The TQn Is Super k-Matching Graph
政 宗 · Advances in Applied Mathematics · 2025
图 G 的整数 k -匹配是由 E( G ) 到 { 0,1,⋯,k } 上的映射 f ，满足对任意点 u ，所有 f( e ) 的加和不超过 k ，其中 f( e ) 之和为所有以点 u 为端点的边 e 。当 k=1 时，整数 k -匹配即为匹配。(强)整数 k -匹配排除数由 m p k ( G ) ( sm p k ( G ) ) 表示，是被一个图删去后该图既不存在完美整数 k -匹配，也不存在几乎完美整数 k -匹配的最小点集(点集与边集)的元素数。Caibing Chang、Xianfu Li and Yan Liu介绍了 sm p k ( T Q n ) 。本文提出超强整数 k -匹配的定义并证明 T Q n 是超强整数 k -匹配图。An integer k -matching of a graph G is a function f from E( G ) to { 0,1,⋯,k } such that the sum of f( e ) is not more than k for any vertex u , where the sum of f( e ) is taken over all edges e incident to u . When k=1 , the integer k -matching is a matching. The (strong) integer k -matching preclusion number, denoted by m p k ( G ) ( sm p k ( G ) ) , is the number of elements of the minimum vertex (vertices and edges) whose deletion results in a graph with neither perfect integer k -matching nor almost perfect integer k -matching. The sm p k ( T Q n ) was introduced by Caibing Chang, Xianfu Li and Yan Liu. In this paper, we denote the super strong integer k -matching and prove that T Q n is super strong integer k -matching graph.