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. In this paper, we find this number for the alternating group graphs, Cayley graphs generated by 2-trees and the (n, k)-arrangement graphs. Moreover, we classify all the optimal solutions. . Downloaded from www.worldscientific.com by UNIVERSITY OF AUCKLAND LIBRARY -SERIALS UNIT on 02/03/15. For personal use only. 1414 E. Cheng et al. then it has an even number of vertices; if a graph has an almost-perfect matching, then it has an odd number of vertices. The matching preclusion number of a graph G, denoted by mp(G), is the minimum number of edges whose deletion leaves the resulting graph without a perfect matching or almost-perfect matching. Any such optimal set is called an optimal matching preclusion set. We define mp(G) = 0 if G has neither a perfect matching nor an almost-perfect matching. This concept of matching preclusion was introduced by Brigham, Harary, Violin and Yellen [5]. They introduced this concept as a measure of robustness in the event of edge failure in interconnection networks, as well as a theoretical connection to conditional connectivity, "changing and unchanging of invariants" and extremal graph theory. We refer the readers to [5] for details and additional references. In [5], the matching preclusion number was determined for three classes of graphs, namely, the complete graphs, the complete bipartite graphs and the hypercubes; in addition, all the optimal solutions were found. Useful distributed processor architectures offer the advantage of improved connectivity and reliability. An important component of such a distributed system is the system topology, which defines the inter-processor communication architecture. In the area of interconnection networks, hypercubes are classical. In the late 1980s and early 1990s, the star graphs (Akers, Harel and Krishnamurthy [1]) and the alternating group graphs (Jwo, Lakshmibarahan and Dhall [12]) were introduced as better alternatives than the hypercubes. Indeed, they have shown to be superior to the hypercubes in many ways. Later, two generalizations were introduced, namely, the (n, k)-star graphs (Chiang and Chen [9]) generalizing the star graphs and the arrangement graphs (Day and Tripathi [10]) generalizing both the star graphs and the alternating group graphs. They formed the core classes of interconnection networks. These networks have since generated a considerable amount of research including fault tolerant routings, strong connectivity properties, various Hamiltonian properties, broadcasting, orientation, and embedding. In certain applications, every vertex requires a special partner at any given time and the matching preclusion number measures the robustness of this requirement in the event of link failures as indicated in [5]. Hence in these interconnection networks, it is desirable to have the property that the only optimal matching preclusion sets are those whose ele...