On the algebraic connectivity of graphs as a function of genus
TLDR
In this paper, the algebraic connectivity of graphs of various genus has been studied and an upper bound on the connectivity of complete graphs of a fixed genus k is given, and the values of k for which the upper bound can be attained.About:
This article is published in Linear Algebra and its Applications.The article was published on 2006-12-01 and is currently open access. It has received 17 citations till now. The article focuses on the topics: Chordal graph & Indifference graph.read more
Citations
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Old and new results on algebraic connectivity of graphs
TL;DR: A survey of algebraic connectivity of a graph G is given in this paper, where the second smallest eigenvalue of the Laplacian of the graph G, denoted a(G), is considered.
A Survey of Automated Conjectures in Spectral Graph Theory
TL;DR: In this article, the authors present a survey and a discussion of the results about graph eigenvalues that were first conjectured using computer programs, such as GRAPH, Graffiti, Ingrid, newGRAPH and AutoGraphiX.
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A survey of automated conjectures in spectral graph theory
TL;DR: A survey and a discussion of results about graph eigenvalues first conjectured, and in some cases proved, using computer programs, such as GRAPH, Graffiti, Ingrid, newGRAPH and AutoGraphiX are presented.
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Complexity of Earth Surface System Evolutionary Pathways
TL;DR: The Spectral radius measures structural complexity and is highest for fully connected, lowest for linear sequential and cyclic graphs, and intermediate for divergent and convergent patterns as discussed by the authors, indicating inferential synchronization and is inversely related to historical contingency.
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Circulant graphs and tessellations on flat tori
TL;DR: In this paper, the diameter of a circulant graph is characterized as quotient lattices, which are realized as vertices connected by a knot on a k-dimensional flat torus tessellated by hypercubes or hyperparallelotopes.
References
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Book
Introduction to Graph Theory
TL;DR: In this article, the authors introduce the concept of graph coloring and propose a graph coloring algorithm based on the Eulers formula for k-chromatic graphs, which can be seen as a special case of the graph coloring problem.
Book
Nonnegative Matrices in the Mathematical Sciences
TL;DR: 1. Matrices which leave a cone invariant 2. Nonnegative matrices 3. Semigroups of non negative matrices 4. Symmetric nonnegativeMatrices 5. Generalized inverse- Positivity 6. M-matrices 7. Iterative methods for linear systems 8. Finite Markov Chains
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Algebraic connectivity of graphs
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Laplacian matrices of graphs: a survey
TL;DR: In this paper, the authors survey some of the many results known for Laplacian matrices, and present a survey of the most important results in the field of graph analysis.