Effect of Edge Deletion and Addition on Zagreb Indices of Graphs

A characterization of trees based on edge-deletion and its applications for domination-type invariants

Discrete Applied Mathematics ◽

10.1016/j.dam.2021.04.020 ◽

2021 ◽

Vol 299 ◽

pp. 50-61

Author(s):

Michitaka Furuya

Keyword(s):

Edge Deletion

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Some graph operations in multiplicative Zagreb indices

10.1063/5.0025250 ◽

2020 ◽

Author(s):

M. Radhakrishnan ◽

M. Suresh ◽

V. Mohana Selvi

Keyword(s):

Zagreb Indices ◽

Graph Operations

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Mathematical Properties of Variable Topological Indices

Symmetry ◽

10.3390/sym13010043 ◽

2020 ◽

Vol 13 (1) ◽

pp. 43

Author(s):

José M. Sigarreta

Keyword(s):

Real Number ◽

Large Class ◽

Symmetric Functions ◽

Topological Indices ◽

Current Interest ◽

Zagreb Indices ◽

Mathematical Properties ◽

Connectivity Indices ◽

Optimal Bounds ◽

New Framework

A topic of current interest in the study of topological indices is to find relations between some index and one or several relevant parameters and/or other indices. In this paper we study two general topological indices Aα and Bα, defined for each graph H=(V(H),E(H)) by Aα(H)=∑ij∈E(H)f(di,dj)α and Bα(H)=∑i∈V(H)h(di)α, where di denotes the degree of the vertex i and α is any real number. Many important topological indices can be obtained from Aα and Bα by choosing appropriate symmetric functions and values of α. This new framework provides new tools that allow to obtain in a unified way inequalities involving many different topological indices. In particular, we obtain new optimal bounds on the variable Zagreb indices, the variable sum-connectivity index, the variable geometric-arithmetic index and the variable inverse sum indeg index. Thus, our approach provides both new tools for the study of topological indices and new bounds for a large class of topological indices. We obtain several optimal bounds of Aα (respectively, Bα) involving Aβ (respectively, Bβ). Moreover, we provide several bounds of the variable geometric-arithmetic index in terms of the variable inverse sum indeg index, and two bounds of the variable inverse sum indeg index in terms of the variable second Zagreb and the variable sum-connectivity indices.

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On multiplicative degree based topological indices for planar octahedron networks

Main Group Metal Chemistry ◽

10.1515/mgmc-2020-0026 ◽

2020 ◽

Vol 43 (1) ◽

pp. 219-228

Author(s):

Ghulam Dustigeer ◽

Haidar Ali ◽

Muhammad Imran Khan ◽

Yu-Ming Chu

Keyword(s):

Graph Theory ◽

Information Science ◽

Biological Activities ◽

Molecular Graph ◽

Triangular Prism ◽

Structure Property ◽

Zagreb Index ◽

Zagreb Indices ◽

Chemical Graph Theory ◽

Analytical Formulas

AbstractChemical graph theory is a branch of graph theory in which a chemical compound is presented with a simple graph called a molecular graph. There are atomic bonds in the chemistry of the chemical atomic graph and edges. The graph is connected when there is at least one connection between its vertices. The number that describes the topology of the graph is called the topological index. Cheminformatics is a new subject which is a combination of chemistry, mathematics and information science. It studies quantitative structure-activity (QSAR) and structure-property (QSPR) relationships that are used to predict the biological activities and properties of chemical compounds. We evaluated the second multiplicative Zagreb index, first and second universal Zagreb indices, first and second hyper Zagreb indices, sum and product connectivity indices for the planar octahedron network, triangular prism network, hex planar octahedron network, and give these indices closed analytical formulas.

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