Nordhaus-Gaddum relations for proximity and remoteness in graphs

DOI10.1016/j.camwa.2010.02.001zbMath1193.05092OpenAlexW2065561033MaRDI QIDQ988253

Pierre Hansen, Mustapha Aouchiche

Publication date: 26 August 2010

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2010.02.001

zbMATH Keywords

proximityextremal graphremotenessNordhaus-Gaddum

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Distance in graphs (05C12)

Related Items

Remoteness and distance, distance (signless) Laplacian eigenvalues of a graph, Proximity in triangulations and quadrangulations, Proximity, remoteness and distance eigenvalues of a graph, Minimum status of series-reduced trees with given parameters, On the extremal properties of the average eccentricity, On autographix conjecture regarding domination number and average eccentricity, On the difference between proximity and other distance parameters in triangle-free graphs and \(C_4\)-free graphs, Minimum status of trees with a given degree sequence, Proof of conjectures involving algebraic connectivity of graphs, Proximity and average eccentricity of a graph, Proofs of the AutoGraphiX conjectures on the domination number, average eccentricity and proximity, Proof of conjectures on remoteness and proximity in graphs, Which numbers are status differences?, Variable neighbourhood search: methods and applications, Proximity, remoteness and girth in graphs, Proximity and remoteness in triangle-free and \(C_4\)-free graphs in terms of order and minimum degree, Variable neighbourhood search: Methods and applications, Proximity and remoteness in graphs: Results and conjectures, Proximity, remoteness and minimum degree, The difference between remoteness and radius of a graph

Uses Software

• AutoGraphiX

Cites Work

• Eigenvalue problems of Nordhaus--Gaddum type
• Maximum induced trees in graphs
• Some parameters of graph and its complement
• Radius, diameter, and minimum degree
• Variable neighborhood search
• A note on Nordhaus-Gaddum inequalities for domination.
• Variable neighborhood search for extremal graphs. V: Three ways to automate finding conjectures
• A sharp upper bound for the spectral radius of the Nordhaus-Gaddum type
• Variable neighborhood search for extremal graphs. I: The AutoGraphiX system
• Nordhaus-Gaddum results for restrained domination and total restrained domination in graphs
• Proximity and remoteness in graphs: Results and conjectures
• On Complementary Graphs
• AutoGraphiX: a survey
• Variable neighborhood search: Principles and applications
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