Characterizing the negative inertia index of connected graphs in terms of their girth

DOI10.1016/j.disc.2024.113997zbMATH Open1539.0502MaRDI QIDQ6542021

Fang Duan

Publication date: 21 May 2024

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

zbMATH Keywords

extremal graphsgirthpositive inertia indexnegative inertia index

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Enumeration in graph theory (05C30) Paths and cycles (05C38) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Distance in graphs (05C12) Connectivity (05C40) Graphical indices (Wiener index, Zagreb index, Randi? index, etc.) (05C09)

Cites Work

• A characterization of graphs with rank 4
• On connected graphs of order \(n\) with girth \(g\) and nullity \(n-g\)
• On graphs with a fixed number of negative eigenvalues
• Graphs with a small number of nonnegative eigenvalues
• Positive and negative inertia index of a graph
• On the smallest positive eigenvalue of bipartite unicyclic graphs with a unique perfect matching
• Graphs \(G\) with nullity \(n(G) - g(G) -1\)
• On connected signed graphs with rank equal to girth
• The inertia of weighted unicyclic graphs
• Signed graphs with small positive index of inertia
• On the nullity of graphs
• Matrix Analysis
• Graphs with Exactly Two Negative Eigenvalues
• Characterization of graphs with exactly two non-negative eigenvalues
• On graphs with girth \(g\) and positive inertia index of \(\frac{\lceil g\rceil}{2}-1\) and \(\frac{\lceil g\rceil}{2}\)

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