Relationship between the rank and the matching number of a graph

DOI10.1016/j.amc.2019.02.055zbMath1428.05190OpenAlexW2921469655WikidataQ128264174 ScholiaQ128264174MaRDI QIDQ2011117

Jing Huang, Xiao-Bing Luo, Shuchao Li, Zhimin Feng

Publication date: 28 November 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2019.02.055

zbMATH Keywords

rankmatching numbernullity

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70)

Related Items (8)

Relation between the inertia indices of a complex unit gain graph and those of its underlying graph ⋮ Relations between the inertia indices of a mixed graph and those of its underlying graph ⋮ The multiplicity of an \(A_\alpha \)-eigenvalue: a unified approach for mixed graphs and complex unit gain graphs ⋮ Unnamed Item ⋮ Bounds for the rank of a complex unit gain graph in terms of its maximum degree ⋮ On the characteristic polynomials and \(H\)-ranks of the weighted mixed graphs ⋮ Some mixed graphs with \(H\)-rank 4, 6 or 8 ⋮ Bounds on the nullity, the H-rank and the Hermitian energy of a mixed graph

Uses Software

• AutoGraphiX

Cites Work

• 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
• A characterization of graphs with rank 5
• A characterization of graphs \(G\) with nullity \(|V(G)|-2m(G)+2c(G)\)
• A characterization of graphs with rank 4
• On the nullity of tricyclic graphs
• On the nullity of a graph with cut-points
• Relation between the skew-rank of an oriented graph and the independence number of its underlying graph
• On the relationship between the skew-rank of an oriented graph and the rank of its underlying graph
• On the nullity and the matching number of unicyclic graphs
• On the nullity of bicyclic graphs
• On the nullity of graphs with pendent vertices
• The rank of a graph after vertex addition
• Variable neighborhood search for extremal graphs. V: Three ways to automate finding conjectures
• The rank of a signed graph in terms of the rank of its underlying graph
• Chromatic number and the 2-rank of a graph
• The nullity of \((k-1)\)-cyclic graphs
• Variable neighborhood search for extremal graphs. I: The AutoGraphiX system
• Bounds for the matching number, the edge chromatic number and the independence number of a graph in terms of rank
• An upper bound for the nullity of a bipartite graph in terms of its maximum degree
• Skew-rank of an oriented graph with edge-disjoint cycles
• The nullity ofk-cyclic graphs of ∞-type
• On the nullity of graphs
• The skew-rank of oriented graphs
• On the nullity of bipartite graphs
• On the nullity of graphs with pendant trees
• Skew-rank of an oriented graph in terms of matching number
• Relation between the skew-rank of an oriented graph and the rank of its underlying graph
• The extremal graphs with respect to their nullity
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Relationship between the rank and the matching number of a graph