The distance spectral gap of a connected graph is defined as the difference between its first and second distance eigenvalues. In this note, the unique \(n\)-vertex trees with minimal and maximal distance spectral gaps, and the unique \(n\)-vertex unicyclic graph with minimal distance spectral gap are determined.
Citation
Rundan Xing. Note on the Distance Spectral Gap of Graphs[J], Ars Combinatoria, Volume 133. 247-253. .