6 citations · 8 across the 8 of their papers we have counts for
8 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…
On Neumaier Cayley graphs
Rhys J. Evans, Sergey Goryainov, Grigory Ryabov +1
In the present paper, we study Neumaier Cayley graphs. First, we give a criterion for a Cayley graph to be a Neumaier graph with a spread given by the cosets of a subgroup. Further…
A census of Cayley graphs
Rhys J. Evans, Primož Potočnik
Given positive integers and , we present methods to construct all groups of order at most that contain a Cayley set of size , and to enumerate the Cayley sets of orde…
Tightness of the weight-distribution bound for strongly regular polar graphs
Rhys J. Evans, Sergey Goryainov, Leonid Shalaginov
In this paper we show the tightness of the weight-distribution bound for the positive non-principle eigenvalue of strongly regular (affine) polar graphs and characterise the optima…
Equitable 2-partitions of the Johnson graphs
Rhys J. Evans, Alexander L. Gavrilyuk, Sergey Goryainov +1
We finish the classification of equitable 2-partitions of the Johnson graphs of diameter 3, , for .
Bounds for regular induced subgraphs of strongly regular graphs
Rhys J. Evans
Given feasible strongly regular graph parameters and a non-negative integer , we determine upper and lower bounds on the order of a -regular induced subgraph of a…
A general construction of strictly Neumaier graphs and a related switching
Rhys J. Evans, Sergey Goryainov, Elena V. Konstantinova +1
We present a construction of Neumaier graphs with nexus 1, which generalises two known constructions of Neumaier graphs. We also use W. Wang, L. Qiu, and Y. Hu switching to show th…
The smallest strictly Neumaier graph and its generalisations
Rhys J. Evans, Sergey Goryainov, Dmitry Panasenko
A regular clique in a regular graph is a clique such that every vertex outside of the clique is adjacent to the same positive number of vertices inside the clique. We continue the…