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Graph theory continues to be one of the fastest growing areas of modern mathematics because of its wide applicability in such diverse disciplines as computer science, engineering, chemistry, management science,  social science, and resource planning. Graphs arise as mathematical models in these fields, and the theory of graphs provides a spectrum of methods of proof. This concisely written textbook is intended for an introductory course in gra...

Mathematics in the Real World is a self-contained, accessible introduction to the world of mathematics for non-technical majors. With a focus on everyday applications and context, the topics in this textbook build in difficulty and are presented sequentially, starting with a brief review of sets and numbers  followed by an introduction to elementary statistics, models, and graph theory. Data and identification numbers are then covered, providi...

Magic squares are among the more popular mathematical recreations. Over the last 50 years, many generalizations of "magic" ideas have been applied to graphs. Recently there has been a resurgence of interest in "magic labelings" due to a number of results that have applications to the problem of decomposing graphs into trees. Key features of this second edition include: ·         a new chapter on magic labeling of directed graphs ·         app...

This book has grown out of graduate courses given by the author at Southern Illinois University, Carbondale, as well as a series of seminars delivered at Curtin University of Technology, Western Australia. The book is intended to be used both as a textbook at the graduate level and also as a professional reference. The topic of one-factorizations fits into the theory of combinatorial designs just as much as it does into graph theory. Factors a...

Wallis's book on discrete mathematics is a resource for an introductory course in a subject fundamental to both mathematics and computer science, a course that is expected not only to cover certain specific topics but also to introduce students to important modes of thought specific to each discipline . . . Lower-division undergraduates through graduate students.—Choice (Review of the First Edition) Very appropriately entitled as a 'beginner's...

“The present textbook gives a concise introduction to finite mathematics. It covers the topics counting, discrete probability, graph theory, linear equations, and linear programming…The mathematical level seems higher than the average US textbook on this topic. It is well written and easy to read, with many examples and applications.”  –Internationale Mathematische Nachrichten (Review of First Edition) “This book is designed for an elementary ...

The Mathematics of Elections and Voting  takes an in-depth look at the mathematics in the context of voting and electoral systems, with focus on simple ballots, complex elections, fairness,  approval voting,  ties, fair and unfair voting, and manipulation techniques. The exposition opens with a sketch of the mathematics behind the various methods used in conducting elections. The reader is lead to a comprehensive picture of the theoretical bac...

An advanced reference containing 21 selected or consolidated papers presented at an international conference in April 1988 at Tunxi (now Hunangshan), China. Contains recent, previously unavailable findings of Chinese mathematicians, discusses problems, results, and proving methods of combinatorial d

This book has grown out of graduate courses given by the author at Southern Illinois University, Carbondale, as well as a series of seminars delivered at Curtin University of Technology, Western Australia. The book is intended to be used both as a textbook at the graduate level and also as a professional reference. The topic of one-factorizations fits into the theory of combinatorial designs just as much as it does into graph theory. Factors a...

Preliminaries.- Room Squares.- Sum-Free Sets.- Hadamard Matrices.- Aftermath.

Graphic sequences.- Combinatorics ¿ A branch of group theory?.- The current status of the generalised moore graph problem.- Some 2-(2n+1, n, n-1) designs with multiple extensions.- The graph of type (0, ?, ?) realizations of a graphic sequence.- Divisibility properties of some fibonacci-type sequences.- Interlaced trees: A class of graceful trees.- Construction of balanced designs and related identities.- A generalization of a covering problem...

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Comma-free codes and incidence algebras.- Non-orthogonal graeco-latin designs.- An infinite family of skew weighing matrices.- Some elementary aspects of the catalan numbers.- Some new constructions for orthogonal designs.- Bounds of finite relations.- Products of graphs and their spectra.- Some computational results on the spectra of graphs.- A non-imbeddable proper colouring.- Minimal degree of primitive permutation groups.- Number of factor...