Distance-Regular Graphs

In theoretical medicine, topological indices are defined to test the medicine and pharmacy characteristics, such as melting point, boiling point, toxicity and other biological activities. As basic molecular structures, hexagonal jagged-rectangle and distance-regular structure are widely appeared in medicine, pharmacy and biology engineering. In this paper, we study the chemical properties of hexagonal jagged-rectangle from the mathematical point of view. Several vertex distance-based indices are determined. Furthermore, the Wiener related indices of distance-regular structure are also considered.

Characteristics studies of molecular structures in drugs.

Strongly Regular Graphs and Partial Geometries

This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A., Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.

Distance-regular graphs

Pseudo-skeleton approximations with better accuracy estimates

On the structure of connected locally GQ (3, 9)-graphs

On the geometricity of distance-regular graphs without 4-claws

We consider undirected graphs without loops and multiple edges. Previously, V. P. Burichenko and A. A. Makhnev [1] found intersection arrays of distance-regular locally cyclic graphs with the number of vertices at most 1000. It is shown that the automorphism group of a graph with intersection array {15, 12, 1; 1, 2, 15}, {35, 32, 1; 1, 2, 35}, {39, 36, 1; 1, 2, 39}, or {42, 39, 1; 1, 3, 42} (such a graph enters the above-mentioned list) acts intransitively on the set of its vertices.

A. A. Makhnev

Papers

On the structure of connected locally GQ (3, 9)-graphs

On the geometricity of distance-regular graphs without 4-claws

Automorphism Groups of Small Distance-Regular Graphs

Automorphisms of a strongly regular graph with parameters (392, 115, 18, 40)

On automorphisms of a strongly regular graph with parameters (88, 27, 6, 9)