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 amply regular locally GQ (4, 8)-graphs

Graphs of diameter at most 3 whose local subgraphs are pseudogeometric graphs for pG s − 3 ( s , t )

Pseudogeometric graph for pG 4 (8, 175)

On automorphisms of a distance-regular graph with intersection array {15, 12, 1; 1, 4, 15}

Let M be the class of strongly regular graphs for which μ is a nonprincipal eigenvalue. Note that the neighborhood of any vertex of an AT4-graph lies in M. Parameters of graphs from M were described earlier. We find intersection arrays of small AT4-graphs and of strongly regular graphs corresponding to them.

A. A. Makhnev

Papers

On amply regular locally GQ (4, 8)-graphs

Graphs of diameter at most 3 whose local subgraphs are pseudogeometric graphs for pG s − 3 ( s , t )

Pseudogeometric graph for pG 4 (8, 175)

On automorphisms of a distance-regular graph with intersection array {15, 12, 1; 1, 4, 15}

Small AT4-graphs and strongly regular subgraphs corresponding to them