Extremal trees of given segment sequence with respect to some eccentricity-based invariants

Zhang, Minjie; Wang, Chengyong; Li, Shuchao

doi:10.1016/j.dam.2020.03.018

Cited by 6 publications

(1 citation statement)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For quite a long time, researchers have been interested in the computation of topological indices, which is mainly related to the applications of these topological indices in nonempirical quantitative structure property relationships and quantitative structure activity relationships. Hundreds of topological indices have been introduced and studied, one may refer to [18,22,24,[41][42][43] for some recent results.…”

Section: Background and Definitionsmentioning

confidence: 99%

On the Harary Index of Graphs with Given Dissociation Number

Huang¹,

Zhang²

2023

MATCH

View full text Add to dashboard Cite

For a graph G = (VG, EG), a subset S ⊆ VG is called a maximum dissociation set if the induced subgraph G[S] does not contain P3 as its subgraph, and the subset has maximum cardinality. The dissociation number of G is the number of vertices in a maximum dissociation set of G. This paper mainly studies the problem of determining the maximum or minimum values of the Harary indices among all trees, bipartite graphs and general connected graphs with fixed order and dissociation number. To be specific, we determine the sharp upper bound of the Harary index among all connected graphs (resp. bipartite graphs, trees) with given order and dissociation number. The extremal graphs meeting these upper bounds are fully characterized. Furthermore, the graphs having the minimum Harary indices with fixed order n and dissociation number φ ∈ {2, 2 3 n , n − 2, n − 1} are also showed. * J.

show abstract