گراف‌های صفر-متقارن: نمایش‌های منظم گرافیکی سه‌وجهی گروه‌ها

Zero-Symmetric Graphs: Trivalent Graphical Regular Representations of Groups describes the zero-symmetric graphs with not more than 120 vertices.The graphs considered in this text are finite, connected, vertex-transitive and trivalent. This book is organized into three parts encompassing 25 chapters. The first part reviews the different classes of zero-symmetric graphs, according to the number of essentially different edges incident at each vertex, namely, the S, T, and Z classes. The remaining two parts discuss the theorem and characteristics of type 1Z and 3Z graphs. These parts explore Cayley graphs of specific groups, including the parameters of Cayley graphs of groups. This book will prove useful to mathematicians, computer scientists, and researchers. Content: Front Matter, Page iii Copyright, Page iv Dedication, Page v Preface, Page ix 1 - INTRODUCTION, Pages 3-5 2 - CAYLEY GRAPHS (IN GENERAL), Pages 6-8 3 - TRIVALENT CAYLEY GRAPHS; THE LCF AND FRUCHT NOTATIONS, Pages 9-16 4 - GENERAL REMARKS ON 0-SYMMETRIC GRAPHS, Pages 17-20 5 - GENERAL REMARKS ON GRAPHS OF TYPE 1Z, Pages 23-26 6 - ZERO-SYMMETRIC GRAPHS OF GIRTH 3, Pages 27-29 7 - THE GROUPS Z(m,n,k), Pages 30-34 8 - GRAPHS OF TYPE 1Z AND GIRTH 4 THAT ARE CAYLEY GRAPHS OF GROUPS Z(m,2,k), Pages 35-40 9 - GRAPHS OF TYPE 1Z THAT ARE CAYLEY GRAPHS OF GROUPS Z(m,n,k), n > 2, Pages 41-47 10 - MORE 0-SYMMETRIC CAYLEY GRAPHS OF Z(m,n,k) OBTAINED BY CHANGE OF GENERATORS, Pages 48-50 11 - THE JUXTAPOSITION PROCEDURE, Pages 51-53 12 - THE CAYLEY GRAPHS OF THE GROUPS F3,2,-1 AND F4,2,1; THE EXTENDED LCF NOTATION, Pages 54-59 13 - THE PARAMETERS OF CAYLEY GRAPHS OF GROUPS WITH THREE INVOLUTORY GENERATORS, Pages 63-70 14 - THE COMPANION GRAPHS OF CAYLEY GRAPHS OF GIRTH 4, Pages 71-73 15 - THE CAYLEY GRAPHS OF COXETER'S GROUPS Gp,q,r, Pages 74-83 16 - A PROCEDURE FOR OBTAINING BIPARTITE CAYLEY GRAPHS OF GIRTH 4, Pages 84-89 17 - THE CAYLEY GRAPHS OF THE GROUPS B(m,k), Pages 90-100 18 - CAYLEY GRAPHS OF DIRECT PRODUCTS OF DIHEDRAL GROUPS, Pages 101-106 19 - MORE 0-SYMMETRIC GRAPHS OF GIRTH 4 WITH 96 OR 120 VERTICES, Pages 107-115 20 - COMPANION GRAPHS OF HIGHER GIRTH, Pages 116-119 21 - PRELIMINARIES ON CAYLEY GRAPHS OF GIRTH 6 FOR DIHEDRAL AND RELATED GROUPS, Pages 120-125 22 - CAYLEY GRAPHS OF DIHEDRAL GROUPS WITH ONE REDUNDANT GENERATOR, Pages 126-140 23 - CAYLEY GRAPHS OF DIHEDRAL GROUPS WITH NO REDUNDANT GENERATOR, Pages 141-143 24 - CAYLEY GRAPHS OF GENERALIZED DIHEDRAL GROUPS, Pages 144-152 25 - YET ANOTHER 0-SYMMETRIC GRAPH WITH 96 VERTICES, Pages 153-154 TABLES, Pages 155-164 BIBLIOGRAPHY, Pages 165-168 Index, Pages 169-170 H.s.m. Coxeter, Roberto Frucht, David L. Powers. Includes Index. Bibliography: 165-168.