Algebraic Combinatorics and Spectral Graph Theory
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Algebra, Geometry and Topology".
Deadline for manuscript submissions: 20 April 2025 | Viewed by 12
Special Issue Editors
Interests: spectral graph theory; quantum mechanics; networks; carbon molecules; molecular conductivity
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
Algebraic combinatorics lies at the crossroads of algebra and combinatorics, exploiting the interaction between these two vast areas of mathematics. By combining tools and methods from both areas, discrete structures are studied through the application of either algebraic methods in combinatorial contexts or of combinatorial techniques in algebraic settings. A vast array of areas, including but not limited to representation theory, knot theory, symmetric functions, and mathematical physics, are closely linked with algebraic combinatorics. The combinatorial properties of discrete structures, in general, and of graphs, in particular, can be expressed using eigenvalues and eigenvectors of matrices related to these structures/graphs. This approach was first introduced in the late 1980s in an attempt to prove Cheeger’s inequality for finding a sparse cut. The most common matrices associated with a graph are the adjacency matrix and the Laplacian matrix. Once the eigenvalues and eigenvectors of such matrices are computed (or estimated), these can be related to structural properties of graphs. For example, it is a well-known result of Fiedler (1973) that the second smallest eigenvalue of the Laplacian matrix of a graph is positive if and only if the graph is connected. It is indeed the case that some of the most useful and beautiful applications of spectral graph theory are combinatorial.
Prof. Dr. Irene Sciriha
Dr. John Gauci
Guest Editors
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Keywords
- eigenvalues of a graph/digraph
- spectral graph theory
- sum of the k largest eigenvalues/singular values
- energy of a graph/digraph
- distance
- distance energy
- topological indices
- extremal graphs/digraphs
- spectral determination
- complex networks
- complex systems
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