Degree-based topological indices: Optimal trees with given number of pendents

Goubko, Mikhail; Gutman, Iván

doi:10.1016/j.amc.2014.04.081

Cited by 22 publications

(17 citation statements)

References 17 publications

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“…One can show that s(T Nevertheless, within the class of trees T there is a relation between the parameters m(T ), s(T ) and (T ), which we will explore in the rest part of this section. The lower bounds for both Zagreb indices of a tree in terms of its number of leaves have been obtained previously and are summarized in the following theorem: Theorem 13 ( [28]). For any tree T with = (T ) leaves, the following statements hold:…”

Section: Relations With Maximum-leaf Spanning Treesmentioning

confidence: 99%

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Scale-free spanning trees: complexity, bounds and algorithms

Orlovich¹,

Kirill²,

Kaibel³

et al. 2020

Preprint

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We introduce and study the general problem of finding a most "scale-free-like" spanning tree of a connected graph. It is motivated by a particular problem in epidemiology, and may be useful in studies of various dynamical processes in networks. We employ two possible objective functions for this problem and introduce the corresponding algorithmic problems termed m-SF and s-SF Spanning Tree problems. We prove that those problems are APX-and NP-hard, respectively, even in the classes of cubic, bipartite and split graphs. We study the relations between scalefree spanning tree problems and the max-leaf spanning tree problem, which is the classical algorithmic problem closest to ours. For split graphs, we explicitly describe the structure of optimal spanning trees and graphs with extremal solutions. Finally, we propose two Integer Linear Programming formulations and two fast heuristics for the s-SF Spanning Tree problem, and experimentally assess their performance using simulated and real data.

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Section: Relations With Maximum-leaf Spanning Treesmentioning

confidence: 99%

“…The problem of maximization of the objective (24) subject to the constraints ( 23), (26) with auxiliary variables (25) will be further referred to as Martin formulation, and the problem with the same objective subject to the constraints ( 23), (28) with auxiliary variables (27) as Miller -Tucker -Zemlin or MTZ formulation.…”

Section: Synthetic Graphsmentioning

confidence: 99%

Scale-free spanning trees: complexity, bounds and algorithms

Orlovich¹,

Kirill²,

Kaibel³

et al. 2020

Preprint

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“…1 Also of interest is to maximize and minimize chemically relevant degree-based indices on trees with a fixed number of leaves. In [5], the author finds the maximum and minimum of the first Zagreb index (the sum of squares of vertex degrees) on trees with a fixed number of leaves. The search for such trees was then extended to other degree-based invariants [6], but not to the ABC index.…”

Section: Introductionmentioning

confidence: 99%

Which tree has the smallest ABC index among trees with k leaves?

Magnant

Nowbandegani

Gutman

2015

Discrete Applied Mathematics

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a b s t r a c tGiven a graph G, the atom-bond connectivity (ABC ) index is defined to be ABCwhere u and v are vertices of G, d(u) denotes the degree of the vertex u, and u ∼ v indicates that u and v are adjacent. Although it is known that among trees of a given order n, the star has maximum ABC index, we show that if k ≤ 18, then the star of order k+1 has minimum ABC index among trees with k leaves. If k ≥ 19, then the balanced double star of order k + 2 has the smallest ABC index.

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“…The history and the mathematical concepts for graph theory are discussed in [1][2][3]. These days, computation of topological indices for different chemical structures is an important task as discussed in [4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Zagreb Connection Number Index of Nanotubes and Regular Hexagonal Lattice

Qureshi

Fahad

et al. 2019

Open Chemistry

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Topological indices are the fixed numbers associated with the graphs. In recent years, mathematicians used indices to check the pharmacology characteristics and molecular behavior of medicines. In this article the first Zagreb connection number index is computed for the nanotubes VC5C7[ p, q] , HC5C7[ p,q] and Boron triangular Nanotubes. Also, the same index is computed for the Quadrilateral section $P_{m}^{n}$and $P_{m+\frac{1}{2}}^{n}$cuts from regular hexagonal lattices.

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Degree-based topological indices: Optimal trees with given number of pendents

Cited by 22 publications

References 17 publications

Scale-free spanning trees: complexity, bounds and algorithms

Scale-free spanning trees: complexity, bounds and algorithms

Which tree has the smallest ABC index among trees with k leaves?

Zagreb Connection Number Index of Nanotubes and Regular Hexagonal Lattice

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