Topic
Odd graph
About: Odd graph is a research topic. Over the lifetime, 1188 publications have been published within this topic receiving 34824 citations.
Papers published on a yearly basis
1 / 2
Papers
Book•
1 Jan 2009
TL;DR: The Laplacian of a Graph and Cuts and Flows are compared to the Rank Polynomial.
Abstract: Graphs.- Groups.- Transitive Graphs.- Arc-Transitive Graphs.- Generalized Polygons and Moore Graphs.- Homomorphisms.- Kneser Graphs.- Matrix Theory.- Interlacing.- Strongly Regular Graphs.- Two-Graphs.- Line Graphs and Eigenvalues.- The Laplacian of a Graph.- Cuts and Flows.- The Rank Polynomial.- Knots.- Knots and Eulerian Cycles.- Glossary of Symbols.- Index.
9,212 citations
16 May 1974
TL;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.
3,236 citations
28 Aug 2006
TL;DR: In the information age, graph theory has been studied in a variety of ways as mentioned in this paper, e.g., the preferential attachment scheme for biological networks, random graphs with given expected degrees, the rise of the giant component Average distance and the diameter Eigenvalues of the adjacency matrix of $G(\mathbf{w})$ The semi-circle law for $G(m)$ The configuration model for power law graphs.
Abstract: Graph theory in the information age Old and new concentration inequalities A generative model--the preferential attachment scheme Duplication models for biological networks Random graphs with given expected degrees The rise of the giant component Average distance and the diameter Eigenvalues of the adjacency matrix of $G(\mathbf{w})$ The semi-circle law for $G(\mathbf{w})$ Coupling on-line and off-line analyses of random graphs The configuration model for power law graphs The small world phenomenon in hybrid graphs Bibliography Index.
967 citations
TL;DR: An O(mn) algorithm is presented to determine whether a graph G with m edges and n vertices has an odd cycle transversal of order at most k, for any fixed k, and an algorithm is obtained that determines a graph has a half integral packing of odd cycles of weight k.
523 citations
[...]
395 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 4 |
| 2023 | 5 |
| 2022 | 14 |
| 2021 | 9 |
| 2020 | 5 |
| 2019 | 7 |