Introduction

Armen H. Zemanian
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Armen H. Zemanian: University at Stony Brook, Electrical Engineering Department

Chapter 1 in Pristine Transfinite Graphs and Permissive Electrical Networks, 2001, pp 1-16 from Springer

Abstract: Abstract This introductory chapter does three things. The first section surveys much of the technical phrases, notations, and symbols used in this book. Sections 1.2 and 1.3 are motivational and are addressed to those readers unfamiliar with transfinite graphs and networks. It presents basic ideas in a leisurely, informal fashion and argues for some sympathy toward our subject. On the other hand, Section 1.4 is addressed to those having prior knowledge of transfinite graphs. It defines a pristine graph and shows how any transfinite graph can be converted into a pristine one without any disruption in the connectedness structure of the graph. Thus, our restriction to pristine graphs throughout this book does not compromise generality so far as connectedness issues are concerned; moreover, that restriction does in fact simplify much of the theory of transfinite graphs.

Keywords: Pristine Graph; Infinite Graph; Extraction Path; Positive Natural Number; Shunting Conductance (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0163-2_1

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DOI: 10.1007/978-1-4612-0163-2_1

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