A characterization for a graph with an eigenvalue of multiplicity \(2c(G)+p(G) - 1\)

DOI10.1016/J.DISC.2024.114028zbMATH Open1539.05092MaRDI QIDQ6542049

Dein Wong, Jinxing Zhao, Yuanshuai Zhang

Publication date: 21 May 2024

Published in: Discrete Mathematics (Search for Journal in Brave)

zbMATH Keywords

eigenvalue multiplicityParter-Wiener theoremstar complement theory

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Connectivity (05C40)

Cites Work

• Title not available (Why is that?)
• Nullity of a graph in terms of the dimension of cycle space and the number of pendant vertices
• On multiple eigenvalues of trees
• Graphs \(G\) with nullity \(2c(G) + p(G) - 1\)
• Graphs with nullity \(2c(G)+p(G)-1\)
• Graphs with eigenvalue \(-1\) of multiplicity \(2 \theta (G)+ \rho (G) -1\)
• The leaf-free graphs with nullity \(2 c ( G ) - 1\)
• The multiplicity of an arbitrary eigenvalue of a graph in terms of cyclomatic number and number of pendant vertices
• The Parter--Wiener Theorem: Refinement and Generalization
• On the multiplicity of −1 as an eigenvalue of a tree with given number of pendant vertices

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