Discrete Mathematics

Discrete mathematics, in contrast with continuous mathematics, concerns countable objects which have isolated values not varying continuously. Some examples of discrete structures are integer sequences, finite set systems, permutations and graphs. The primary research focus of the discrete math group is Graph Theory, which is a highly active area of current research in the field. Graphs are abstractions of real-world networks, and Graph Theory is the mathematical foundation of network science. It provides mathematical tools and techniques to deeply analyze all sorts of complex networks and develop algorithms to solve problems arising in them. 

 

The discrete math group at USU addresses algebraic, enumerative, structural and extremal aspects of graphs and has a broad range of research interests which include graph polynomials, chromatic graph theory, matching theory, independence and domination in graphs, graph homomorphisms,  graph connectivity, average graph parameters, algebraic representations of graphs via matrices, directed graphs, tournaments and variations on interval graphs.