Integer k-matching preclusion of graphs

As a generalization of matching preclusion number of a graph, we provide the (strong) integer $k$-matching preclusion number, abbreviated as $MP^{k}$ number ($SMP^{k}$ number), which is the minimum number of edges (vertices and edges) whose deletion results in a graph that has neither perfect integer $k$-matching nor almost perfect integer $k$-matching. In this paper, we show that when $k$ is even, the ($SMP^{k}$) $MP^{k}$ number is equal to the (strong) fractional matching preclusion number. We obtain a necessary condition of graphs with an almost-perfect integer $k$-matching and a relational expression between the matching number and the integer $k$-matching number of bipartite graphs. Thus the $MP^{k}$ number and the $SMP^{k}$ number of complete graphs, bipartite graphs and arrangement graphs are obtained, respectively.Comment: 18 pages, 5 figure

Fractional strong matching preclusion for two variants of hypercubes

Let F be a subset of edges and vertices of a graph G. If G-F has no fractional perfect matching, then F is a fractional strong matching preclusion set of G. The fractional strong matching preclusion number is the cardinality of a minimum fractional strong matching preclusion set. In this paper, we mainly study the fractional strong matching preclusion problem for two variants of hypercubes, the multiply twisted cube and the locally twisted cube, which are two of the most popular interconnection networks. In addition, we classify all the optimal fractional strong matching preclusion set of each

Matching Preclusion of the Generalized Petersen Graph

The matching preclusion number of a graph with an even number of vertices is the minimum number of edges whose deletion results in a graph with no perfect matchings. In this paper we determine the matching preclusion number for the generalized Petersen graph $P(n,k)$ and classify the optimal sets

Conditional Strong Matching Preclusion of the Alternating Group Graph

The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. Park and Ihm introduced the problem of strong matching preclusion under the condition that no isolated vertex is created as a result of faults. In this paper, we find the conditional strong matching preclusion number for the $n$-dimensional alternating group graph $AG_n$

Fractional matching preclusion for butterfly derived networks

The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. As a generalization, Liu and Liu [18] recently introduced the concept of fractional matching preclusion number. The fractional matching preclusion number (FMP number) of G, denoted by fmp(G), is the minimum number of edges whose deletion leaves the resulting graph without a fractional perfect matching. The fractional strong matching preclusion number (FSMP number) of G, denoted by fsmp(G), is the minimum number of vertices and edges whose deletion leaves the resulting graph without a fractional perfect matching. In this paper, we study the fractional matching preclusion number and the fractional strong matching preclusion number for butterfly network, augmented butterfly network and enhanced butterfly network

The Conditional Strong Matching Preclusion of Augmented Cubes

The strong matching preclusion is a measure for the robustness of interconnection networks in the presence of node and/or link failures. However, in the case of random link and/or node failures, it is unlikely to find all the faults incident and/or adjacent to the same vertex. This motivates Park et al. to introduce the conditional strong matching preclusion of a graph. In this paper we consider the conditional strong matching preclusion problem of the augmented cube $AQ_n$, which is a variation of the hypercube $Q_n$ that possesses favorable properties