Isomorphisms, Symmetry and Computations in Algebraic Graph Theory

This book consists of a selection of peer-reviewed contributions to the Workshop on Algebraic Graph Theory that took place in Pilsen, Czech Republic in October 2016. Primarily intended for early career researchers, it presents eight self-contained articles on a selection of topics within algebraic combinatorics, ranging from association schemes to symmetries of graphs and isomorphism testing. Algebraic combinatorics is a compelling mathematical discipline based on the powerful interplay of algebraic and combinatorial methods. Algebraic interpretation of combinatorial structures (such as symmetry or regularity) has often led to enlightening discoveries and powerful results, while discrete and combinatorial structures have given rise to new algebraic structures that have found valuable applications. In addition to these original research contributions, the reader will find a survey linking numerous threads in algebraic combinatorics, and an extensive tutorial showcasing the universality of algebraic methods in the study of combinatorial structures.

Inhalt
G. Erskine, K. Hriáková, J. irá, Orientably-regular maps on twisted linear fractional groups.- V. Gatt, M. Klin, J. Lauri, V. Liskovets, From Schur rings to constructive and analytical enumeration of circulant graphs with prime-cubed number of vertices.- . Gyürki, A note on a problem of L. Martnez on almost-uniform partial sum families.- . Gyürki, M. Klin, M. Ziv-Av, The Paulus-Rozenfeld-Thompson graph on 26 vertices revisited and related combinatorial structures.- G. A. Jones, Paley and the Paley graphs.- M. E. Muzychuk, Automorphism groups of Paley graphs and cyclotomic schemes.- R. Nedela, I. Ponomarenko, Recognizing and testing isomorphism of Cayley graphs over an abelian group of order 4p in polynomial time.- S. Reichard, Tatra schemes and their mergings.