Graph Theory and Calculus: Ratios of Classes of Graphs - Softcover

Paul Winter

Softcover

ISBN 10: 3659707708 ISBN 13: 9783659707704

Publisher: LAP LAMBERT Academic Publishing, 2015

Synopsis

Graph Theory and Calculus Ratios of Classes of Graphs

About this title

About the Author

Paul August Winter is an honorary senior research associate, of the School of Mathematics, Statistics and Computer Science, at the University of Kwa-Zulu Natal, Durban, South Africa, where he has taught mathematics for over four decades. His research areas are Graph Theory, Combinatorics, Design Theory and the Psychology of Mathematics Education. He has publications in mathematics education, graph theory and combinatorics in local and international journals.

From the Back Cover

This book is suitable for both undergraduate students (first year calculus and undergraduate graph theory) and post-graduate students (algebraic graph theory and combinatorics).
The main thrust of the book involves the join between graph theory and calculus, by introducing 10 different ratios involving graph theoretical concepts. When these ratios are a function f(n), of the order n of graphs G belonging to a class of graphs, then the horizontal asymptotic behavior of f(n) becomes significant in terms of practical applications, when a large number of vertices are involved, such as in networks, or molecules with a large number of atoms. Moreover, by attaching the average degree of G (the length of G) to the Riemann integral of f(n) (the height of G) the idea of area becomes relevant in terms of this ratio involving such classes of graphs.
These ratios have realized such aspects as:

• Asymptotic convergence of 1/e identical to the famous secretary problem.
  
• The class of eigen-bibalanced graphs, and the complement of such classes of graphs, being connected by a function which is an involution.
  
• Sequences, as a subsequence of the Farey sequence- Farey sequences are named after the British geologist John Farey, Sr.
  
• The formation energy of a graph in terms the graph's H-decomposable parts.
  
• Domination aspect, involving the chromatic number (or energy) of the cover graph of G (the subgraph of G induced by a minimum 2 or 3 vertex cover of G) in relation to G or the complete graph when a large number of vertices are involved.
  
• A unit-trigonometrical equation.
  
• Differential equations having solutions with asymptotic convergence identical to the convergence of ratios of classes of graphs.
  

From the Inside Flap

Acknowledgements
I would like to thank Carol Lynne Jessop, Fadekemi Janet Adewusi, Samson Ogagoghene Ojako, Professor Dinesh Sarvate and Dr Costas Zachariades for their contributions to articles in this book. Working with them was a wonderful experience and we learnt much from each other while investigating the new and fascinating different ratios.
Finally I wish to thank the mathematics department of UKZN for the use of their facilities.

Edition details

• Publisher: LAP LAMBERT Academic Publishing
• Publication date: 2015
• Language: English
• ISBN 10: 3659707708
• ISBN 13: 9783659707704
• Binding: Paperback
• Number of pages: 216