The project is focused on algebraic and spectral methods, their study and applications in the design and analysis of models of networks, molecules and other discrete structures with given properties, with emphasis on the following two areas:
(a) investigation of extremal constructions of vertex-transitive and Cayley graphs and their automorphism groups (focusing mainly on the covering-space construction methods) in the degree-diameter and the degree-girth problems,
(b) investigation of invertibility of graphs and related spectral estimates, construction of infinite classes of invertible graphs, and development of a new methodology of inverting graphs with singular associated matrices.