Spectral results on regular graphs with (k,τ)-regular sets

A set of vertices S@?V(G) is (k,@t)-regular if it induces a k-regular subgraph of G such that |N"G(v)@?S|=@t@?v@?S. Note that a connected graph with more than one edge has a perfect matching if and only if its line graph has a (0,2)-regular set. In this paper, some spectral results on the adjacency matrix of graphs with (k,@t)-regular sets are presented. Relations between the combinatorial structure of a p-regular graph with a (k,@t)-regular set and the eigenspace corresponding to each eigenvalue @l@?{p,k-@t} are deduced. Finally, additional results on the effects of Seidel switching (with respect to a bipartition induced by S) of regular graphs are also introduced.