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Finite Graphs and Networks

Finite Graphs and Networks PDF Author: Robert G. Busacker
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 320

Book Description


Finite Graphs and Networks

Finite Graphs and Networks PDF Author: Robert G. Busacker
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 320

Book Description


Graphs, Networks and Algorithms

Graphs, Networks and Algorithms PDF Author: Dieter Jungnickel
Publisher: Springer Science & Business Media
ISBN: 3662038226
Category : Mathematics
Languages : en
Pages : 597

Book Description
Revised throughout Includes new chapters on the network simplex algorithm and a section on the five color theorem Recent developments are discussed

Graphs and Networks

Graphs and Networks PDF Author: Armen H. Zemanian
Publisher: Springer Science & Business Media
ISBN: 0817681787
Category : Mathematics
Languages : en
Pages : 207

Book Description
This self-contained book examines results on transfinite graphs and networks achieved through continued research effort over the past several years. These new results, covering the mathematical theory of electrical circuits, are different from those presented in two previously published books by the author, Transfiniteness for Graphs, Electrical Networks, and Random Walks and Pristine Transfinite Graphs and Permissive Electrical Networks. Specific topics covered include connectedness ideas, distance ideas, and nontransitivity of connectedness. The book will appeal to a diverse readership, including graduate students, electrical engineers, mathematicians, and physicists working on infinite electrical networks. Moreover, the growing and presently substantial number of mathematicians working in nonstandard analysis may well be attracted by the novel application of the analysis employed in the work.

Finite Graphs and Networks: an Introduction with Application

Finite Graphs and Networks: an Introduction with Application PDF Author: Robert G. Busacker
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

Book Description


Finite Graphs Networks: An Introduction With Applications

Finite Graphs Networks: An Introduction With Applications PDF Author: R.G. Busacker
Publisher:
ISBN:
Category :
Languages : it
Pages : 0

Book Description


The Mathematics of Finite Networks

The Mathematics of Finite Networks PDF Author: Michael Rudolph
Publisher: Cambridge University Press
ISBN: 1009287834
Category : Computers
Languages : en
Pages :

Book Description
Since the early eighteenth century, the theory of networks and graphs has matured into an indispensable tool for describing countless real-world phenomena. However, the study of large-scale features of a network often requires unrealistic limits, such as taking the network size to infinity or assuming a continuum. These asymptotic and analytic approaches can significantly diverge from real or simulated networks when applied at the finite scales of real-world applications. This book offers an approach to overcoming these limitations by introducing operator graph theory, an exact, non-asymptotic set of tools combining graph theory with operator calculus. The book is intended for mathematicians, physicists, and other scientists interested in discrete finite systems and their graph-theoretical description, and in delineating the abstract algebraic structures that characterise such systems. All the necessary background on graph theory and operator calculus is included for readers to understand the potential applications of operator graph theory.

Finite graphs and networks

Finite graphs and networks PDF Author: Robert G. Busacker
Publisher:
ISBN:
Category :
Languages : en
Pages : 320

Book Description


Finite Graphs and Network

Finite Graphs and Network PDF Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 294

Book Description


Large Networks and Graph Limits

Large Networks and Graph Limits PDF Author: László Lovász
Publisher: American Mathematical Soc.
ISBN: 0821890859
Category : Mathematics
Languages : en
Pages : 495

Book Description
Recently, it became apparent that a large number of the most interesting structures and phenomena of the world can be described by networks. To develop a mathematical theory of very large networks is an important challenge. This book describes one recent approach to this theory, the limit theory of graphs, which has emerged over the last decade. The theory has rich connections with other approaches to the study of large networks, such as ``property testing'' in computer science and regularity partition in graph theory. It has several applications in extremal graph theory, including the exact formulations and partial answers to very general questions, such as which problems in extremal graph theory are decidable. It also has less obvious connections with other parts of mathematics (classical and non-classical, like probability theory, measure theory, tensor algebras, and semidefinite optimization). This book explains many of these connections, first at an informal level to emphasize the need to apply more advanced mathematical methods, and then gives an exact development of the theory of the algebraic theory of graph homomorphisms and of the analytic theory of graph limits. This is an amazing book: readable, deep, and lively. It sets out this emerging area, makes connections between old classical graph theory and graph limits, and charts the course of the future. --Persi Diaconis, Stanford University This book is a comprehensive study of the active topic of graph limits and an updated account of its present status. It is a beautiful volume written by an outstanding mathematician who is also a great expositor. --Noga Alon, Tel Aviv University, Israel Modern combinatorics is by no means an isolated subject in mathematics, but has many rich and interesting connections to almost every area of mathematics and computer science. The research presented in Lovasz's book exemplifies this phenomenon. This book presents a wonderful opportunity for a student in combinatorics to explore other fields of mathematics, or conversely for experts in other areas of mathematics to become acquainted with some aspects of graph theory. --Terence Tao, University of California, Los Angeles, CA Laszlo Lovasz has written an admirable treatise on the exciting new theory of graph limits and graph homomorphisms, an area of great importance in the study of large networks. It is an authoritative, masterful text that reflects Lovasz's position as the main architect of this rapidly developing theory. The book is a must for combinatorialists, network theorists, and theoretical computer scientists alike. --Bela Bollobas, Cambridge University, UK

Transfiniteness

Transfiniteness PDF Author: Armen H. Zemanian
Publisher: Springer Science & Business Media
ISBN: 1461207673
Category : Mathematics
Languages : en
Pages : 252

Book Description
"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.