Constructing the Mate of Cospectral 5-regular Graphs with and without a Perfect Matching

The problem of finding a perfect matching in an arbitrary simple graph is well known and popular theory. It used various fields, such as chemistry, combinatorics, game theory etc. M G set pairwise nonadjacent edges, ie, those that do not have common vertices. Matching called if it covers all vertices the graph, ie each incidental to exactly one edges. By Koenig's theorem, regular bipartite graphs positive degree always matching. However, are need further research.
 Another interesting search for nonisomorphic cospectral graphs. In addition, find additional properties. For example, with without matching.
 fact there pair connected k-regular had been investigated by Blazsik, Cummings Haemers. 5-regular constructed using Godsil-McKay switching paper.