Extremal total distance of graphs of given radius I. Issue 1 (3rd November 2020)

• Record Type: Journal Article
• Authors: Cambie, Stijn
• Is Part Of: Journal of graph theory. Volume 97:Issue 1(2021)
• Page Start: 104
• Page End: 122
• Publication Date: 2020-11-03
• Subjects: digraph -- graph -- radius -- total distance -- wiener index; Graph theory -- Periodicals; 511
• DOI: 10.1002/jgt.22644
• Languages: English
• ISSNs: 0364-9024

Abstract

Abstract: In 1984, Plesník determined the minimum total distance for given order and diameter and characterized the extremal graphs and digraphs. We prove the analog for given order and radius, when the order is sufficiently large compared to the radius. This confirms asymptotically a conjecture of Chen et al. We also state an analog of the conjecture of Chen et al for digraphs and prove it for sufficiently large order.