On connected graphs of order \(n\) with girth \(g\) and nullity \(n-g\)

DOI10.1016/J.LAA.2021.07.005zbMath1473.05196OpenAlexW3188648783MaRDI QIDQ820992

Dein Wong, Qi Zhou, Bit-Shun Tam

Publication date: 29 September 2021

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

Full work available at URL: https://doi.org/10.1016/j.laa.2021.07.005

zbMATH Keywords

rankgirthshortest cyclenullity of a graph

Mathematics Subject Classification ID

Paths and cycles (05C38) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Structural characterization of families of graphs (05C75) Distance in graphs (05C12) Connectivity (05C40) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (8)

Graphs \(G\) with nullity \(n(G) - g(G) -1\) ⋮ On connected signed graphs with rank equal to girth ⋮ On graphs with girth \(g\) and positive inertia index of \(\frac{\lceil g\rceil}{2}-1\) and \(\frac{\lceil g\rceil}{2}\) ⋮ On connected \(\mathbb{T}\)-gain graphs with rank equal to girth ⋮ Unnamed Item ⋮ Characterizing the negative inertia index of connected graphs in terms of their girth ⋮ The gap between the rank of a complex unit gain graph and its underlying graph ⋮ On extremal graphs for zero forcing number

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