On Regular Generalized Line Graph Designs
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Author | : Ching-Shui Cheng |
Publisher | : |
Total Pages | : 22 |
Release | : 1982 |
Genre | : |
ISBN | : |
Download On Regular Generalized Line Graph Designs Book in PDF, Epub and Kindle
A class of efficient designs called regular generalized line graph designs are introduced. This class of designs includes many well-known optimum and efficient designs, e.g., balanced incomplete block designs, group-divisible designs with lambda 2 equal lambda 1 + 1, group-divisible designs with lambda 1 equal lambda 2 + 1 and group size two, triangular designs with lambda 2 equal lambda 1 + 1, L2 designs with lambda 2 equal lambda 1 + 1, etc. The optimality of regular generalized line graph designs is investigated. This uses graph theory as a tool and unifies much of the previous work in the area. (Author).
Author | : Dragoš Cvetkovic |
Publisher | : Cambridge University Press |
Total Pages | : 316 |
Release | : 2004-07-22 |
Genre | : Mathematics |
ISBN | : 9780521836630 |
Download Spectral Generalizations of Line Graphs Book in PDF, Epub and Kindle
Introduction -- Forbidden subgraphs -- Root systems -- Regular graphs -- Star complements -- The Maximal exceptional graphs -- Miscellaneous results.
Author | : North-Holland Publishing Company |
Publisher | : |
Total Pages | : 1006 |
Release | : 2002 |
Genre | : |
ISBN | : |
Download Journal of Statistical Planning and Inference Book in PDF, Epub and Kindle
Author | : |
Publisher | : |
Total Pages | : 196 |
Release | : 1982 |
Genre | : Science |
ISBN | : |
Download Technical Abstract Bulletin Book in PDF, Epub and Kindle
Author | : Mohra Abdullah Alqahtani |
Publisher | : |
Total Pages | : 137 |
Release | : 2018 |
Genre | : Graph connectivity |
ISBN | : |
Download Generalized Line Graphs Book in PDF, Epub and Kindle
With every nonempty graph, there are associated many graphs. One of the best known and most studied of these is the line graph L (G) of a graph G, whose vertices are the edges of G and where two vertices of L (G) are adjacent if the corresponding edges of G are adjacent. This concept was implicitly introduced by Whitney in 1932. Over the years, characterizations of graphs that are line graphs have been given, as well as graphs whose line graphs have some specified property. For example, Beineke characterized graphs that are line graphs by forbidding certain graphs that can be subgroups. Sedlacek characterized those graphs whose line graph is planar. Harary and Nash-Williams characterized those graphs whose line graph is Hamiltonian. Chartrand and Wall proved that if G is a connected graph all of whose vertices have degree 3 or more, then, although L(G) may not be Hamiltonian, the line graph of L(G) must be Hamiltonian. Over the years, various generalizations of line graphs have been introduced and studied by many. Among them are Schwenk graphs and k-line graphs introduced in 2015 and 2016 here at Western Michigan University. This study introduces a generalization of line graphs and discusses several well-known structural properties of this class of graphs. Furthermore, it establishes a number of characterizations of connected graphs whose generalized line graphs possess some prescribed graph structure.
Author | : Andries E. Brouwer |
Publisher | : Springer Science & Business Media |
Total Pages | : 513 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642743412 |
Download Distance-Regular Graphs Book in PDF, Epub and Kindle
Ever since the discovery of the five platonic solids in ancient times, the study of symmetry and regularity has been one of the most fascinating aspects of mathematics. Quite often the arithmetical regularity properties of an object imply its uniqueness and the existence of many symmetries. This interplay between regularity and symmetry properties of graphs is the theme of this book. Starting from very elementary regularity properties, the concept of a distance-regular graph arises naturally as a common setting for regular graphs which are extremal in one sense or another. Several other important regular combinatorial structures are then shown to be equivalent to special families of distance-regular graphs. Other subjects of more general interest, such as regularity and extremal properties in graphs, association schemes, representations of graphs in euclidean space, groups and geometries of Lie type, groups acting on graphs, and codes are covered independently. Many new results and proofs and more than 750 references increase the encyclopaedic value of this book.
Author | : |
Publisher | : |
Total Pages | : 1134 |
Release | : 1989 |
Genre | : Aeronautics |
ISBN | : |
Download Scientific and Technical Aerospace Reports Book in PDF, Epub and Kindle
Author | : Lowell W. Beineke |
Publisher | : Springer Nature |
Total Pages | : 301 |
Release | : 2021-10-29 |
Genre | : Mathematics |
ISBN | : 303081386X |
Download Line Graphs and Line Digraphs Book in PDF, Epub and Kindle
In the present era dominated by computers, graph theory has come into its own as an area of mathematics, prominent for both its theory and its applications. One of the richest and most studied types of graph structures is that of the line graph, where the focus is more on the edges of a graph than on the vertices. A subject worthy of exploration in itself, line graphs are closely connected to other areas of mathematics and computer science. This book is unique in its extensive coverage of many areas of graph theory applicable to line graphs. The book has three parts. Part I covers line graphs and their properties, while Part II looks at features that apply specifically to directed graphs, and Part III presents generalizations and variations of both line graphs and line digraphs. Line Graphs and Line Digraphs is the first comprehensive monograph on the topic. With minimal prerequisites, the book is accessible to most mathematicians and computer scientists who have had an introduction graph theory, and will be a valuable reference for researchers working in graph theory and related fields.
Author | : Andries E. Brouwer |
Publisher | : Springer Science & Business Media |
Total Pages | : 254 |
Release | : 2011-12-17 |
Genre | : Mathematics |
ISBN | : 1461419395 |
Download Spectra of Graphs Book in PDF, Epub and Kindle
This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association schemes, p-ranks of configurations and similar topics. Exercises at the end of each chapter provide practice and vary from easy yet interesting applications of the treated theory, to little excursions into related topics. Tables, references at the end of the book, an author and subject index enrich the text. Spectra of Graphs is written for researchers, teachers and graduate students interested in graph spectra. The reader is assumed to be familiar with basic linear algebra and eigenvalues, although some more advanced topics in linear algebra, like the Perron-Frobenius theorem and eigenvalue interlacing are included.
Author | : Alan Jerome Hoffman |
Publisher | : World Scientific |
Total Pages | : 492 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 9812796932 |
Download Selected Papers of Alan Hoffman with Commentary Book in PDF, Epub and Kindle
Dr Alan J Hoffman is a pioneer in linear programming, combinatorial optimization, and the study of graph spectra. In his principal research interests, which include the fields of linear inequalities, combinatorics, and matrix theory, he and his collaborators have contributed fundamental concepts and theorems, many of which bear their names. This volume of Dr Hoffman's selected papers is divided into seven sections: geometry; combinatorics; matrix inequalities and eigenvalues; linear inequalities and linear programming; combinatorial optimization; greedy algorithms; graph spectra. Dr Hoffman has supplied background commentary and anecdotal remarks for each of the selected papers. He has also provided autobiographical notes showing how he chose mathematics as his profession, and the influences and motivations which shaped his career. Contents: The Variation of the Spectrum of a Normal Matrix (with H W Wielandt); Integral Boundary Points of Convex Polyhedra (with J Kruskal); On Moore Graphs with Diameters 2 and 3 (with R R Singleton); Cycling in the Simplex Algorithm; On Approximate Solutions of Systems of Linear Inequalities; On the Polynomial of a Graph; Some Recent Applications of the Theory of Linear Inequalities of Extremal Combinatorial Analysis; On Simple Linear Programming Problems; Self-Orthogonal Latin Squares (with R K Brayton & D Coppersmith); On the Nonsingularity of Complex Matrices (with P Camion); A Generalization of Max Flow-Min Cut; A Characterization of Comparability Graphs and of Interval Graphs (with P C Gilmore); and 33 other papers. Readership: Researchers in linear programming and inequalities, combinatorics, combinatorial optimization, graph theory, matrix theory and operations research.