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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Peter Dankelmann
Department of Pure and Applied Mathematics, University of Johannesburg, P.O. Box 524, Auckland Park, Johannesburg 2006, South Africa
Electrical & Electronics Engineering

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Proximity in triangulations and quadrangulations Éva Czabarka; Peter Dankelmann; Trevor Olsen; László Székely
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2022.10.2.7

Abstract

Let G be a connected graph. If σ(v) denotes the arithmetic mean of the distances from v to all other vertices of G, then the proximity, π(G), of G is defined as the smallest value of σ(v) over all vertices v of G. We give upper bounds for the proximity of simple triangulations and quadrangulations of given order and connectivity. We also construct simple triangulations and quadrangulations of given order and connectivity that match the upper bounds asymptotically and are likely optimal.
Co-Authors Éva Czabarka László Székely Trevor Olsen