Mathematics

On one infinite series of admissible intersection arrays of distance-regular graphs of diameter 5

I. T. Mukhamet'yanov

Lysva Branch of Perm National Research Polytechnic University, Lysva

Abstract: Background. One generalization of one known infinite series of admissible intersection arrays of a bipartite antipodal distance-regular graph is proposed for consideration. The theory of distance-regular graphs is a powerful tool for studying finite groups and a number of combinatorial objects (for example, relational schemes). Materials and methods. Methods for finding the spectrum of a graph and calculating its Krein parameters are used. Results. The spectrum of the graph is found and the non-negativity of its Krein parameters (one of the necessary conditions for the existence of a distance-regular graph) is shown. Conclusions. It is possible to further study the graphs under consideration from the point of view of their automorphism groups, as well as the construction of unknown representatives of the series, or the impossibility of the existence of some representatives.

Keywords: bipartite antipodal distance-regular graph, graph intersection array, Graph eigenvalue, graph spectrum, Krein parameters.

UDC: 519.17

DOI: 10.21685/2072-3040-2022-4-2