A proof of the conjecture regarding the sum of domination number and average eccentricity

DOI10.1016/j.dam.2015.08.002zbMath1329.05229OpenAlexW1228647933WikidataQ123188245 ScholiaQ123188245MaRDI QIDQ908297

Zhibin Du, Aleksandar Ilić

Publication date: 4 February 2016

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.dam.2015.08.002

zbMATH Keywords

distancesdomination numberaverage eccentricityautographix

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Distance in graphs (05C12) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Related Items (14)

The average Steiner 3-eccentricity of block graphs ⋮ Bounds on the sum of domination number and metric dimension of graphs ⋮ On autographix conjecture regarding domination number and average eccentricity ⋮ On two eccentricity-based topological indices of graphs ⋮ On Wiener index and average eccentricity of graphs of girth at least 6 and \((C_4, C_5)\)-free graphs ⋮ Proofs of the AutoGraphiX conjectures on the domination number, average eccentricity and proximity ⋮ Average eccentricity, \(k\)-packing and \(k\)-domination in graphs ⋮ Further results regarding the sum of domination number and average eccentricity ⋮ Complexity of \(k\)-rainbow independent domination and some results on the lexicographic product of graphs ⋮ Average eccentricity, minimum degree and maximum degree in graphs ⋮ The Slater and sub-\(k\)-domination number of a graph with applications to domination and \(k\)-domination ⋮ Constructing uniform central graphs and embedding into them ⋮ Upper bounds on the average eccentricity of \(K_3\)-free and \(C_4\)-free graphs ⋮ The minimum eccentric distance sum of trees with given distance k-domination number

Uses Software

• AutoGraphiX

Cites Work

• On the extremal properties of the average eccentricity
• On the eccentric connectivity index of a graph
• Upper bounds on the average eccentricity
• Ordering unicyclic graphs with large average eccentricities
• On eccentric connectivity index
• Eccentric Connectivity Index of Chemical Trees
• Wiener index of trees: Theory and applications
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