Extremal trees of a given degree sequence or segment sequence with respect to average Steiner 3-eccentricity

Shuchao Li, Xin Liu, Wanting Sun and Lixia Yan

Applied Mathematics and Computation, 2023, vol. 438, issue C

Abstract: The Steiner k-eccentricity of a vertex in a graph G is the maximum Steiner distance over all k-subsets containing the vertex. The average Steiner k-eccentricity of G is the mean value of all vertices’ Steiner k-eccentricities in G. Let Tn be the set of all n-vertex trees, Tn,Δ be the set of n-vertex trees with maximum degree Δ, Tn,Δk be the set of n-vertex trees with exactly k vertices of a given maximum degree Δ, and let MTnk be the set of n-vertex trees with exactly k vertices of maximum degree. In this paper, we first determine the sharp upper bound on the average Steiner 3-eccentricity of n-vertex trees with a given degree sequence. The corresponding extremal graphs are characterized. Consequently, together with majorization theory, all graphs among Tn,Δk (resp. Tn,Δ,MTnk,Tn) having the maximum average Steiner 3-eccentricity are identified. Then we characterize the unique n-vertex tree with a given segment sequence having the minimum average Steiner 3-eccentricity. Finally, we determine all n-vertex trees with a given number of segments having the minimum average Steiner 3-eccentricity.

Keywords: Steiner eccentricity; Degree sequence; Segment sequence; Majorization (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300322006300
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:438:y:2023:i:c:s0096300322006300

DOI: 10.1016/j.amc.2022.127556

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 ().