4 papers
A family of Neumaier graphs containing examples with exactly five eigenvalues
Bart De Bruyn, Rhys J. Evans, Sergey Goryainov +1
A Neumaier graph is an edge-regular graph with a regular clique. Such a graph is said to have parameters if it is a -regular graph on vertices having a clique…
Hoffman colorability of graphs with smallest eigenvalue at least -2
Bart De Bruyn, Thijs van Veluw
In accordance with the Cameron-Goethals-Seidel-Shult Classification Theorem, we extend the characterization of Hoffman colorability of line graphs from (Abiad, Bosma, Van Veluw, 20…
Hoffman colorability of (strongly) regular graphs
Aida Abiad, Bart De Bruyn, Thijs van Veluw
Hoffman's bound is a well-known eigenvalue bound on the chromatic number of a graph. By interpreting this bound as a parameter, we show multiple applications of colorings attaining…
Divisible design graphs with selfloops
Anwita Bhowmik, Bart De Bruyn, Sergey Goryainov
We develop a basic theory for divisible design graphs with possible selfloops (LDDG's), and describe two infinite families of such graphs, some members of which are also classical…