Spectral results on regular graphs with image-regular sets Original Research Article

A set of vertices image is image-regular if it induces a k-regular subgraph of G such that image. Note that a connected graph with more than one edge has a perfect matching if and only if its line graph has a image-regular set. In this paper, some spectral results on the adjacency matrix of graphs with image-regular sets are presented. Relations between the combinatorial structure of a p-regular graph with a image-regular set and the eigenspace corresponding to each eigenvalue image 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.