On a dynamic extension of the theory of graphs

Abstract

We consider a graph of a given order whose topology is dictated by an underlying controlled dynamics. This dynamic graph structure provides a convenient framework for modeling distributed dynamic systems where the topology of the interaction among its elements evolves in time. The static theory of graphs has been an active area of research in non-enumerative combinatorics. In this paper, we propose a framework for studying dynamic graphs as an area that lies at the intersection of dynamical systems and combinatorics. We also highlight the directions which we find to be particularly promising in this venue.