Jack E. Graver's Books

Locally Finite, Planar, Edge-Transitive Graphs

By: Jack E. Graver,Mark E. Watkins

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Locally Finite, Planar, Edge-Transitive Graphs

By: Jack E. Graver,Mark E. Watkins

The nine finite, planar, 3-connected, edge-transitive graphs have been known and studied for many centuries. The infinite, locally finite, planar, 3-connected, edge-transitive graphs can be classified according to the number of their end. The 1-ended graphs in this class were identified by Grünbaum and Shephard; Watkins characterized the 2-ended members. Any remaining graphs in this class must have uncountably may ends. In this work, infinite-ended members of this class are shown to exist. A more detailed classification scheme in terms of the types of Petrie walks in the graphs in this class and the local structure of their automorphism groups is presented.

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Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821805568

ISBN 13

9780821805565

Combinatorial Rigidity

By: Jack E. Graver,Brigitte Servatius,Herman Servatius

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Combinatorial Rigidity

By: Jack E. Graver,Brigitte Servatius,Herman Servatius

This book presents rigidity theory in a historical context. The combinatorial aspects of rigidity are isolated and framed in terms of a special class of matroids, which are a natural generalization of the connectivity matroid of a graph. The book includes an introduction to matroid theory and an extensive study of planar rigidity. The final chapter is devoted to higher dimensional rigidity, highlighting the main open questions. Also included is an extensive annotated bibiolography with over 150 entries. The book is aimed at graduate students and researchers in graph theory and combinatorics or in fields which apply the structural aspects of these subjects in architecture and engineering. Accessible to those who have had an introduction to graph theory at the senior or graduate level, the book would be suitable for a graduate course in graph theory.

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Page Count

184

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821838016

ISBN 13

9780821838013

Counting on Frameworks

Mathematics to Aid the Design of Rigid Structures

By: Jack E. Graver

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Counting on Frameworks

Mathematics to Aid the Design of Rigid Structures

By: Jack E. Graver

Book developing a mathematical theory of rigidity, for undergraduates working in modelling or graph theory.

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Page Count

196

Publisher

Cambridge University Press

Published Date

ISBN 10

0883853310

ISBN 13

9780883853313

Book's by Jack E. Graver

Locally Finite, Planar, Edge-Transitive Graphs

Locally Finite, Planar, Edge-Transitive Graphs

Combinatorial Rigidity

Combinatorial Rigidity

Counting on Frameworks

Counting on Frameworks

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