This book presents and illustrates the main tools and ideas of algebraic graph theory, with a primary emphasis on current rather than classical topics. It is designed to offer self-contained treatment of the topic, with strong emphasis on concrete examples.
The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reorganized.
Foreword The topic of this volume is the connection between graph theory and algebra – more specifically , how algebra helps in the study of graphs , and how graph theory repays the debt . There are two main connections between graph ...
Algebraic Graph Theory
The Paulus–Rozenfeld–Thompson Graph on 26 Vertices Revisited and Related Combinatorial Structures Štefan Gyürki, ... Many special features of the graph T and its group G make it a remarkable object in algebraic graph theory.
This book is about the design and analysis of algebraic algorithms to solve graph problems. The algebraic way of analyzing graph problems can be viewed from the angles of group theory and linear algebra. We will mostly use linear ...
New in the Fourth Edition: Expanded treatment of Ramsey theory Major revisions to the material on domination and distance New material on list colorings that includes interesting recent results A solutions manual covering many of the ...
In E.W. Mayr, G. Schmidt, and G. Tinhofer, editors, Proceedings of WG 1994, Lecture Notes in Computer Science, No. 903, pages 151– 163. Springer, 1994. A. Schürr. Programmed Graph Replacement Systems. In G. Rozenberg, editor, ...
Algebraic Graph Theory
Moreover, the book contains over 600 well thought-out exercises: although some are straightforward, most are substantial, and some will stretch even the most able reader.
5 2 01 31 10 126 IZAxZ2 Х Figure 10.5 : The Jacobson graphs of some specific rings :) Z2 , Z4 , Z2 x Z2 , or Z2 [ x ] / ( x2 ) . Also , they showed that the Jacobson graph of R is connected whenever R is a nonlocal ring , in which case ...