An interrelation between line graphs, eigenvalues, and matroids

DOI10.1016/0095-8956(73)90030-0zbMath0245.05125OpenAlexW2048159843MaRDI QIDQ2555087

Michael Doob

Publication date: 1973

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0095-8956(73)90030-0

Mathematics Subject Classification ID

Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Combinatorial aspects of matroids and geometric lattices (05B35) Graph theory (05C99)

Related Items

Heat conduction on graphs, Perfect state transfer in Laplacian quantum walk, Strong-coupling scales and the graph structure of multi-gravity theories, The biased graphs whose matroids are binary, Dynamical systems associated with adjacency matrices, Exceptional graphs with smallest eigenvalue -2 and related problems, Odd and even cycles in maker-breaker games, Graph spectra in computer science, Signed graphs, Spanning trees and even integer eigenvalues of graphs, Edge-signed graphs with smallest eigenvalue greater than \(-2\), Biased graphs. II: The three matroids, Unification of lower-bound analyses of the lift-and-project rank of combinatorial optimization polyhedra, Characterizing bias matroids, On the adjacency matrix of a block graph, Lower bounds of the Laplacian graph eigenvalues, Graphs with least eigenvalue \(-2\): The star complement technique, Generalizations of line graphs and applications, Excluding a bipartite circle graph from line graphs, The incidence matrix and labellings of a graph, Biased graphs. I: Bias, balance, and gains, On spectral characterization and embeddings of graphs, Generalizations of magic graphs

Cites Work

• Unnamed Item
• Unnamed Item
• On characterizing certain graphs with four eigenvalues by their spectra
• On the Line Graph of a Projective Plane
• On the Line Graph of a Symmetric Balanced Incomplete Block Design
• Lectures on matroids
• A geometric characterization of the line graph of a projective plane