Algebras, Graphs and their Applications

This book introduces the study of algebra induced by combinatorial objects called directed graphs. These graphs are used as tools in the analysis of graph-theoretic problems and in the characterization and solution of analytic problems. The book presents recent research in operator algebra theory connected with discrete and combinatorial mathematical objects. It also covers tools and methods from a variety of mathematical areas, including algebra, operator theory, and combinatorics, and offers numerous applications of fractal theory, entropy theory, K-theory, and index theory.

Algebra on Graphs. Representations and Operator Algebras of Graph Groupoids. Operator Theory on Graphs. Fractal on Graph Groupoids. Entropy Theory on Graphs. Jones Index Theory on Graph Groupoids. Network Theory on Graphs. K-Theory on Graphs.