On the minimum value of sum-Balaban index

Martin Knor, Jaka Kranjc, Riste Škrekovski and Aleksandra Tepeh

Applied Mathematics and Computation, 2017, vol. 303, issue C, 203-210

Abstract: We consider extremal values of sum-Balaban index among graphs on n vertices. We determine that the upper bound for the minimum value of the sum-Balaban index is at most 4.47934 when n goes to infinity. For small values of n we determine the extremal graphs and we observe that they are similar to dumbbell graphs, in most cases having one extra edge added to the corresponding extreme for the usual Balaban index. We show that in the class of balanced dumbbell graphs, those with clique sizes 2log(1+2)4n+o(n) have asymptotically the smallest value of sum-Balaban index. We pose several conjectures and problems regarding this topic.

Keywords: Sum-Balaban index; Extremal graphs; Dumbbell graphs (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300317300553
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:303:y:2017:i:c:p:203-210

DOI: 10.1016/j.amc.2017.01.041

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().