@article {IOPORT.05126287,
    author       = {Goldberg, Felix},
    title        = {On quasi-strongly regular graphs.},
    year         = {2006},
    journal      = {Linear and Multilinear Algebra},
    volume       = {54},
    number       = {6},
    issn         = {0308-1087},
    pages        = {437-451},
    publisher    = {Taylor \& Francis, Abingdon},
    doi          = {10.1080/03081080600867210},
    abstract     = {Summary: We study the quasi-strongly regular graphs, which are a combinatorial generalization of the strongly regular and the distance regular graphs. Our main focus is on quasi-strongly regular graphs of grade 2. We prove a ``spectral gap''-type result for them which generalizes Seidel's well-known formula for the eigenvalues of a strongly regular graph [see {\it J. J. Seidel}, Linear Algebra Appl. 1, 281--298 (1968; Zbl 0159.25403)]. We also obtain a number of necessary conditions for the feasibility of parameter sets and some structural results. We propose the heuristic principle that the quasi-strongly regular graphs can be viewed as a ``lower-order approximation'' to the distance regular graphs. This idea is illustrated by extending a known result from the distance-regular case to the quasi-strongly regular case. Along these lines, we propose a number of conjectures and open problems. Finally, we list all the proper connected quasi-strongly graphs of grade 2 with up to 12 vertices.},
    identifier   = {05126287},
}