Bounding the k-Steiner Wiener and Wiener-Type Indices of Trees in Terms of Eccentric Sequence
| Auteur | DOSSOU OLORY, AUDACE AMEN VIOUTOU | |
| Auteur | DANKELMANN, PETER | |
| Date d'ajout | 2026-06-02T16:06:57Z | |
| Date de disponibilite | 2026-06-02T16:06:57Z | |
| Date de publication | 2021 | |
| Resume | The eccentric sequence of a connected graph G is the nondecreasing sequence of the eccentricities of its vertices. The Wiener index of G is the sum of the distances between all unordered pairs of vertices of G. The unique trees that minimise the Wiener index among all trees with a given eccentric sequence were recently determined by the present authors. In this paper we show that these results hold not only for the Wiener index, but for a large class of distance-based topological indices which we term Wiener-type indices. Particular cases of this class include the hyper-Wiener index, the Harary index, the generalised Wiener index W λ for λ > 0 and λ < 0, and the reciprocal complementary Wiener index. Our results imply and unify known bounds on these Wiener-type indices for trees of given order and diameter. We also present similar results for the k-Steiner Wiener index of trees with a given ec- centric sequence. The Steiner distance of a set A ⊆ V (G) is the minimum number of edges in a subtree of G whose vertex set contains A, and the k-Steiner Wiener index is the sum of distances of all k-element subsets of V (G). As a corollary, we obtain a sharp lower bound on the k-Steiner Wiener index of trees with given order and diameter, and determine in which cases the extremal tree is unique, thereby correcting an error in the literature. | |
| DOI | 10.1007/s10440-021-00383-9 | |
| Autre identifiant | BECDB-13720 | |
| URI | https://dspace.uac.bj/handle/123456789/11734 | |
| Langue | fr | |
| Fait partie de | Acta Applicandae Mathematicae | |
| Sujet | k-Steiner distance · Wiener-type indices · Eccentric sequence · Caterpillar · | |
| Sujet | Extremal tree structures · Hyper-Wiener index · Generalised Wiener index · Diameter · | |
| Sujet | Harary index · Complementary Wiener index | |
| Titre | Bounding the k-Steiner Wiener and Wiener-Type Indices of Trees in Terms of Eccentric Sequence | |
| Type | Article |