Topic

# Line graph

About: Line graph is a(n) research topic. Over the lifetime, 11568 publication(s) have been published within this topic receiving 304137 citation(s).

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##### Papers

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01 Jan 1976-

Abstract: (1977). Graph Theory with Applications. Journal of the Operational Research Society: Vol. 28, Volume 28, issue 1, pp. 237-238.

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7,219 citations

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5,312 citations

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TL;DR: The value of depth-first search or “backtracking” as a technique for solving problems is illustrated by two examples of an improved version of an algorithm for finding the strongly connected components of a directed graph.

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Abstract: The value of depth-first search or “backtracking” as a technique for solving problems is illustrated by two examples. An improved version of an algorithm for finding the strongly connected componen...

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5,156 citations

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01 Jan 1998-

TL;DR: This book presents an account of newer topics, including Szemer'edi's Regularity Lemma and its use; Shelah's extension of the Hales-Jewett Theorem; the precise nature of the phase transition in a random graph process; the connection between electrical networks and random walks on graphs; and the Tutte polynomial and its cousins in knot theory.

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Abstract: The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed account of newer topics, including Szemer\'edi's Regularity Lemma and its use, Shelah's extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. In no other branch of mathematics is it as vital to tackle and solve challenging exercises in order to master the subject. To this end, the book contains an unusually large number of well thought-out exercises: over 600 in total. Although some are straightforward, most of them are substantial, and others will stretch even the most able reader.

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3,714 citations

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01 Jan 1995-

Abstract: Introduction. Basic Concepts of the Spectrum of a Graph. Operations on Graphs and the Resulting Spectra. Relations Between Spectral and Structural Properties of Graphs. The Divisor of a Graph. The Spectrum and the Group of Automorphisms. Characterization of Graphs by Means of Spectra. Spectra Techniques in Graph Theory and Combinatories. Applications in Chemistry an Physics. Some Additional Results. Appendix. Tables of Graph Spectra Biblgraphy. Index of Symbols. Index of Names. Subject Index.

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2,094 citations