A characterization of long graphs of arbitrary rank

DOI10.1016/j.laa.2012.09.017zbMath1257.05090OpenAlexW2010453253MaRDI QIDQ1931744

Yanyan Li

Publication date: 16 January 2013

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

Full work available at URL: https://doi.org/10.1016/j.laa.2012.09.017

zbMATH Keywords

nullity of graphsrank of graphslong graphs

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Distance in graphs (05C12)

Related Items (19)

Characterization of graphs with given order, given size and given matching number that minimize nullity ⋮ Nullity of a graph in terms of the dimension of cycle space and the number of pendant vertices ⋮ Relation between the inertia indices of a complex unit gain graph and those of its underlying graph ⋮ An upper bound of the nullity of a graph in terms of order and maximum degree ⋮ Complex unit gain graphs of rank 2 ⋮ Upper bound of skew energy of an oriented graph in terms of its skew rank ⋮ Proof of a conjecture on the nullity of a graph ⋮ Relation between the trace norm of an oriented graph and its rank ⋮ The positive and the negative inertia index of line graphs of trees ⋮ Characterizations of graphs with given inertia index achieving the maximum diameter ⋮ An improved lower bound for the nullity of a graph in terms of matching number ⋮ Relation between the \(H\)-rank of a mixed graph and the rank of its underlying graph ⋮ Characterization of oriented graphs of rank 2 ⋮ The signature ofk-cyclic graphs of ∞-type ⋮ Nullity of a graph in terms of path cover number ⋮ An upper bound for the nullity of a bipartite graph in terms of its maximum degree ⋮ The leaf-free graphs with nullity \(2 c ( G ) - 1\) ⋮ Characterization of sub-long graphs of arbitrary rank ⋮ The multiplicity of an arbitrary eigenvalue of a graph in terms of cyclomatic number and number of pendant vertices

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