Transfiniteness

For Graphs, Electrical Networks, and Random Walks

By: Armen H. Zemanian

Write A Review

Hardcover | 1 January 1996

At a Glance

Hardcover
260 Pages

Dimensions(cm)
24.77 x 16.51 x 1.91

Hardcover

$84.99

or 4 interest-free payments of $21.25 with

Ships in 5 to 7 business days

"What good is a newborn baby?" Michael Faraday's reputed response when asked, "What good is magnetic induction?" But, it must be admitted that a newborn baby may die in infancy. What about this one- the idea of transfiniteness for graphs, electrical networks, and random walks? At least its bloodline is robust. Those subjects, along with Cantor's transfinite numbers, comprise its ancestry. There seems to be general agreement that the theory of graphs was born when Leonhard Euler published his solution to the "Konigsberg bridge prob lem" in 1736 [8]. Similarly, the year of birth for electrical network theory might well be taken to be 184 7, when Gustav Kirchhoff published his volt age and current laws [ 14]. Ever since those dates until just a few years ago, all infinite undirected graphs and networks had an inviolate property: Two branches either were connected through a finite path or were not connected at all. The idea of two branches being connected only through transfinite paths, that is, only through paths having infinitely many branches was never invoked, or so it appears from a perusal of various surveys of infinite graphs [17], [20], [29], [32]. Our objective herein is to explore this idea and some of its ramifications. It should be noted however that directed graphs having transfinite paths have appeared in set theory [6, Section 4.

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $0.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Mathematics Number Theory Combinatorics & Graph Theory Science Science in General History of Science Engineering & Technology Energy Technology & Engineering Electrical Engineering Applied Mathematics Mathematical Modelling

Electronics & Communications Engineering Communications Engineering & Telecommunications

Other Editions and Formats

Paperback

Published: 10th November 2013

View Product

Preface
Acknowledgments
Introduction	p. 1
Transfinite Graphs	p. 19
Connectedness	p. 47
Finitely Structured Transfinite Graphs	p. 79
Transfinite Electrical Networks	p. 115
Permissively Finitely Structured Networks	p. 157
Transfinite Random Walks	p. 183
Appendix A: Ordinal and Cardinal Numbers	p. 222
Appendix B: Summable Series	p. 229
Appendix C: Irreducible and Reversible Markov Chains	p. 232
Bibliography	p. 235
Index of Symbols	p. 239
Index	p. 241
Table of Contents provided by Blackwell. All Rights Reserved.

Transfiniteness

For Graphs, Electrical Networks, and Random Walks

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

More in Communications Engineering & Telecommunications

Little Blue Dot

How the Global Positioning System Shaped the Modern World

Innovative Computing and Communications

Proceedings of ICICC 2026, Volume 1

Innovative Computing and Communications

Proceedings of ICICC 2026, Volume 3

Theory and Technique for Low Earth Orbit Satellite Internet of Things

Resource Management for Satellite-Terrestrial Vehicular Networks

SpringerBriefs in Computer Science

Digital Sustainability

Legislations, Standards, Solutions and Related Case Studies

Telecommunications

A Systems Approach

Digital Minimalism

Choosing a Focused Life in a Noisy World

iPhone For Seniors For Dummies, 2026 Edition

iPhone for Seniors For Dummies

Hooked

How to Build Habit-Forming Products

Control Systems Engineering 8th Edition

Australia & New Zealand Edition

iPhone For Dummies, 2026 Edition

iPhone for Dummies

A First Course in Digital Communications

Fundamentals of Wireless Communication

Make: Radio

Hands-On Adventures in the Hidden Universe of Radio Waves

Streaming Wars

How Getting Everything We Wanted Changed Entertainment Forever

Code Dependent

Living in the Shadow of AI - Shortlisted for the Women's Prize for Non-Fiction

The Art of Invisibility

World's Most Famous Hacker Teaches You How to Be Safe in the Age of Big Brother and Big Data

How to Build a Billion Dollar App

Discover the Secrets of the Most Successful Entrepreneurs of Our Time

Signal Processing and Biomedical Engineering Research

Applications of Machine Learning Based on Big Data Principles

Intelligent Technologies

Concept, Applications, and Future Directions, Volume 5

Proceedings of 7th International Conference on Computer and Communication Technologies

IC3T 2025

Atlas of AI

Power, Politics, and the Planetary Costs of Artificial Intelligence

Recent Advances in Technology & Management

This product is categorised by