On graphs with equal algebraic and vertex connectivity

DOI10.1016/S0024-3795(01)00312-3zbMath0991.05071MaRDI QIDQ5957182

Bryan L. Shader, Michael Neumann, Stephen J. Kirkland, Jason J. Molitierno

Publication date: 28 August 2002

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

Laplacian matrixalgebraic connectivityundirected unweighted graphvertex connectivity

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Positive matrices and their generalizations; cones of matrices (15B48) Structural characterization of families of graphs (05C75) Connectivity (05C40)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Non-negative matrices and Markov chains. 2nd ed
• Degree maximal graphs are Laplacian integral
• Abschätzungen für die Eigenwerte positiver linearer Operatoren
• Inclusion domains for the eigenvalues of stochastic matrices
• The sharpness of a lower bound on the algebraic connectivity for maximal graphs
• Matrix Analysis
• The Role of the Group Generalized Inverse in the Theory of Finite Markov Chains
• Distances in Weighted Trees and Group Inverse of Laplacian Matrices
• Bounds on the subdominant eigenvalue involving group inverse with applications to graphs
• On a bound on algebraic connectivity: the case of equality

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