Algebraic and Dynamic Graph Algorithms

Abstract

Algebraic graph theory is the study of algebraic methods to solve graph problems. We review algebraic solutions to the main graph problems in the first part of this chapter. Many real-life networks are represented by dynamic graphs in which new vertices/edges may be inserted and some vertices/edges may be deleted as time progresses. We describe few dynamic graph problems that can be solved by dynamic graph algorithms, and finally we give a brief description of the methods used in dynamic algebraic graph algorithms, which are used for dynamic graphs using linear algebraic techniques.