Integer

\nAs a generalization of matching preclusion number of a graph, we provide the (strong) integer k-matching preclusion number, abbreviated as MPk number (SMPk 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 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. And then the MPk number and the SMPk number of complete graphs, bipartite graphs and arrangement graphs are obtained, respectively.\n