On connected \(\mathbb{T}\)-gain graphs with rank equal to girth

DOI10.1016/j.laa.2024.02.022MaRDI QIDQ6204179

Suliman Khan

Publication date: 27 March 2024

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

zbMATH Keywords

rankgirthcyclomatic number\(\mathbb{T}\)-gain graph

Mathematics Subject Classification ID

Trees (05C05) Paths and cycles (05C38) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Distance in graphs (05C12)

Cites Work

• Nullity of a graph in terms of the dimension of cycle space and the number of pendant vertices
• Spectral properties of complex unit gain graphs
• Biased graphs. I: Bias, balance, and gains
• Spektren endlicher Grafen
• On connected graphs of order \(n\) with girth \(g\) and nullity \(n-g\)
• Inertia of complex unit gain graphs
• A note on the nullity of unicyclic signed graphs
• Graphs \(G\) with nullity \(2c(G) + p(G) - 1\)
• Graphs with nullity \(2c(G)+p(G)-1\)
• Nullity and singularity of a graph in which every block is a cycle
• Graphs \(G\) with nullity \(n(G) - g(G) -1\)
• On connected signed graphs with rank equal to girth
• The rank of a complex unit gain graph in terms of the matching number
• Bounds for the rank of a complex unit gain graph in terms of its maximum degree
• No signed graph with the nullity \(\eta(G,\sigma)=|V(G)|-2m(G)+2c(G)-1\)
• Complex unit gain bicyclic graphs with rank 2, 3 or 4
• On the determinant of the Laplacian matrix of a complex unit gain graph
• The rank of a complex unit gain graph in terms of the rank of its underlying graph
• On the rank of weighted graphs
• The nullity of bicyclic signed graphs

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