The rank of a graph after vertex addition

DOI10.1016/S0024-3795(96)00513-7zbMath0884.05061WikidataQ126351574 ScholiaQ126351574MaRDI QIDQ1369345

Valerie A. Miller, Gayla S. Domke, Kevin K. Blount, George J. Davis, Jean H. Bevis

Publication date: 20 October 1997

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

zbMATH Keywords

eigenvalueadjacency matrixrankgraph spectra

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (25)

Behavior of the binary rank of a graph when vertices and edges are added ⋮ The nullity ofk-cyclic graphs of ∞-type ⋮ Bounds for the matching number, the edge chromatic number and the independence number of a graph in terms of rank ⋮ Relation between the inertia indices of a complex unit gain graph and those of its underlying graph ⋮ Characterization of graphs whose signature equals the number of odd cycles ⋮ The rank of a signed graph ⋮ Bounds for the rank of a complex unit gain graph in terms of the independence number ⋮ Some relations between rank of a graph and its complement ⋮ The rank of a complex unit gain graph in terms of the matching number ⋮ The rank of a signed graph in terms of the rank of its underlying graph ⋮ Bounds for the matching number and cyclomatic number of a signed graph in terms of rank ⋮ The rank of a complex unit gain graph in terms of the rank of its underlying graph ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On the spectrum of the normalized graph Laplacian ⋮ Maximal graphs with respect to rank ⋮ Relation between the \(H\)-rank of a mixed graph and the rank of its underlying graph ⋮ No signed graph with the nullity \(\eta(G,\sigma)=|V(G)|-2m(G)+2c(G)-1\) ⋮ Relationship between the rank and the matching number of a graph ⋮ On the relationship between the skew-rank of an oriented graph and the rank of its underlying graph ⋮ Relation between the skew-rank of an oriented graph and the rank of its underlying graph ⋮ Relation between the rank of a signed graph and the rank of its underlying graph ⋮ On the nullity number of graphs ⋮ Skew-rank of an oriented graph in terms of the rank and dimension of cycle space of its underlying graph

Cites Work

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