Topic

# Split graph

About: Split graph is a research topic. Over the lifetime, 3808 publications have been published within this topic receiving 98911 citations.

##### Papers published on a yearly basis

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01 Jan 1980

TL;DR: This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems and remains a stepping stone from which the reader may embark on one of many fascinating research trails.

Abstract: Algorithmic Graph Theory and Perfect Graphs, first published in 1980, has become the classic introduction to the field. This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems. It remains a stepping stone from which the reader may embark on one of many fascinating research trails. The past twenty years have been an amazingly fruitful period of research in algorithmic graph theory and structured families of graphs. Especially important have been the theory and applications of new intersection graph models such as generalizations of permutation graphs and interval graphs. These have lead to new families of perfect graphs and many algorithmic results. These are surveyed in the new Epilogue chapter in this second edition. New edition of the "Classic" book on the topic Wonderful introduction to a rich research area Leading author in the field of algorithmic graph theory Beautifully written for the new mathematician or computer scientist Comprehensive treatment

4,090 citations

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16 May 1974TL;DR: In this article, the authors introduce algebraic graph theory and show that the spectrum of a graph can be modelled as a graph graph, and the spectrum can be represented as a set of connected spanning trees.

Abstract: 1. Introduction to algebraic graph theory Part I. Linear Algebra in Graphic Thoery: 2. The spectrum of a graph 3. Regular graphs and line graphs 4. Cycles and cuts 5. Spanning trees and associated structures 6. The tree-number 7. Determinant expansions 8. Vertex-partitions and the spectrum Part II. Colouring Problems: 9. The chromatic polynomial 10. Subgraph expansions 11. The multiplicative expansion 12. The induced subgraph expansion 13. The Tutte polynomial 14. Chromatic polynomials and spanning trees Part III. Symmetry and Regularity: 15. Automorphisms of graphs 16. Vertex-transitive graphs 17. Symmetric graphs 18. Symmetric graphs of degree three 19. The covering graph construction 20. Distance-transitive graphs 21. Feasibility of intersection arrays 22. Imprimitivity 23. Minimal regular graphs with given girth References Index.

2,924 citations

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23 Jun 1989TL;DR: In this paper, a connected simple graph with vertex set X of diameter d is considered, and the authors define Ri X2 by (x, y) Ri whenever x and y have graph distance.

Abstract: Consider a connected simple graph with vertex set X of diameter d. Define Ri X2 by (x, y) Ri whenever x and y have graph distance

2,264 citations

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01 Jan 1995

TL;DR: The Spectrum and the Group of Automorphisms as discussed by the authors have been used extensively in Graph Spectra Techniques in Graph Theory and Combinatory Applications in Chemistry an Physics. But they have not yet been applied to Graph Spectral Biblgraphy.

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.

2,119 citations

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TL;DR: The consecutive ones test for the consecutive ones property in matrices and for graph planarity is extended to a test for interval graphs using a recently discovered fast recognition algorithm for chordal graphs.

1,622 citations