Finite Graphs and Networks
Title | Finite Graphs and Networks PDF eBook |
Author | Robert G. Busacker |
Publisher | |
Pages | 320 |
Release | 1965 |
Genre | Mathematics |
ISBN |
Graphs and Networks
Title | Graphs and Networks PDF eBook |
Author | Armen H. Zemanian |
Publisher | Springer Science & Business Media |
Pages | 207 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 0817681787 |
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
Title | Finite Graphs and Networks: an Introduction with Application PDF eBook |
Author | Robert G. Busacker |
Publisher | |
Pages | 0 |
Release | 1965 |
Genre | |
ISBN |
Graphs, Networks and Algorithms
Title | Graphs, Networks and Algorithms PDF eBook |
Author | Dieter Jungnickel |
Publisher | Springer Science & Business Media |
Pages | 597 |
Release | 2013-06-29 |
Genre | Mathematics |
ISBN | 3662038226 |
Revised throughout Includes new chapters on the network simplex algorithm and a section on the five color theorem Recent developments are discussed
Finite Graphs Networks: An Introduction With Applications
Title | Finite Graphs Networks: An Introduction With Applications PDF eBook |
Author | R.G. Busacker |
Publisher | |
Pages | 0 |
Release | |
Genre | |
ISBN |
The Mathematics of Finite Networks
Title | The Mathematics of Finite Networks PDF eBook |
Author | Michael Rudolph |
Publisher | Cambridge University Press |
Pages | |
Release | 2022-05-12 |
Genre | Computers |
ISBN | 1009287834 |
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.
Random Walks on Infinite Graphs and Groups
Title | Random Walks on Infinite Graphs and Groups PDF eBook |
Author | Wolfgang Woess |
Publisher | Cambridge University Press |
Pages | 350 |
Release | 2000-02-13 |
Genre | Mathematics |
ISBN | 0521552923 |
The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.