On general reduced second Zagreb index of graphs

Horoldagva, Batmend; Buyantogtokh, Lkhagva; Das, Kinkar Ch.; Lee, Sang-Gu

doi:10.15672/hjms.2019.660

Cited by 6 publications

(11 citation statements)

References 15 publications

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“…Some information about the chemical applications of M 1 and M 2 can be found in [4,5]. These indices have also been the subject of extensive research into their relationship, comparison, and other mathematical properties [6][7][8][9][10][11][12][13][14]. Many existing facts of the Zagreb indices can be found in survey papers [15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Fixed-Order Chemical Trees with Given Segments and Their Maximum Multiplicative Sum Zagreb Index

Ali,

Noureen,

Moeed

et al. 2024

Mathematics

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Topological indices are often used to predict the physicochemical properties of molecules. The multiplicative sum Zagreb index is one of the multiplicative versions of the Zagreb indices, which belong to the class of most-examined topological indices. For a graph G with edge set E={e1,e2,⋯,em}, its multiplicative sum Zagreb index is defined as the product of the numbers D(e1),D(e2),⋯,D(em), where D(ei) is the sum of the degrees of the end vertices of ei. A chemical tree is a tree of maximum degree at most 4. In this research work, graphs possessing the maximum multiplicative sum Zagreb index are determined from the class of chemical trees with a given order and fixed number of segments. The values of the multiplicative sum Zagreb index of the obtained extremal trees are also obtained.

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Section: Introductionmentioning

confidence: 99%

Fixed-Order Chemical Trees with Given Segments and Their Maximum Multiplicative Sum Zagreb Index

Ali,

Noureen,

Moeed

et al. 2024

Mathematics

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“…where α represents a real number. If α is − 1/2, then R − 1/2 (G) is said to be the Randic connectivity index of G. Gutman and Trinajstic presented the first general Zagreb index in 1972 [12]:…”

Section: Introduction and Applicationsmentioning

confidence: 99%

“…and M 2 (G, p), the first Zagreb polynomial and the second Zagreb polynomial [12,17], respectively, are defined as…”

Section: Introduction and Applicationsmentioning

confidence: 99%

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Degree-Based Topological Indices of Boron B12

Saeed

Long

Mufti

et al. 2021

Journal of Chemistry

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Topological index sometimes called molecular descriptor is a numerical value which associates a chemical composition for correlating chemical structure with numerous physical properties, chemical reactivity, or biological activity. In this paper, we study some topological indices of boron and try to correlate the physicochemical properties such as freezing points, boiling points, melting points, infrared spectrum, electronic parameters, viscosity, and density of chemical graphs. We discuss these topological indices, and some of them are mentioned here such as Randic index, the first general Zagreb index, the general sum connectivity index, hyper-Zagreb index (HM), the atom-bond connectivity index (ABC), the geometric-arithmetic index (GA), the harmonic index (H), and the forgotten index (F).

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“…Certainly, the Bollobás -Erdős-Sarkar index is a BID index (here, it needs to be mentioned that the graph invariant BES (l,1) was defined in [29] for any real number l).…”

Section: Introductionmentioning

confidence: 99%

Some Vertex/Edge-Degree-Based Topological Indices of $r$ -Apex Trees

Ali

Iqbal

Raza

et al. 2021

Journal of Mathematics

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In chemical graph theory, graph invariants are usually referred to as topological indices. For a graph G , its vertex-degree-based topological indices of the form BID G = ∑ u v ∈ E G β d u , d v are known as bond incident degree indices, where E G is the edge set of G , d w denotes degree of an arbitrary vertex w of G , and β is a real-valued-symmetric function. Those BID indices for which β can be rewritten as a function of d u + d v − 2 (that is degree of the edge u v ) are known as edge-degree-based BID indices. A connected graph G is said to be r -apex tree if r is the smallest nonnegative integer for which there is a subset R of V G such that R = r and G − R is a tree. In this paper, we address the problem of determining graphs attaining the maximum or minimum value of an arbitrary BID index from the class of all r -apex trees of order n , where r and n are fixed integers satisfying the inequalities n − r ≥ 2 and r ≥ 1 .

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On general reduced second Zagreb index of graphs

Abstract: Recently, Furtula et al.

Cited by 6 publications

References 15 publications

Fixed-Order Chemical Trees with Given Segments and Their Maximum Multiplicative Sum Zagreb Index

Fixed-Order Chemical Trees with Given Segments and Their Maximum Multiplicative Sum Zagreb Index

Degree-Based Topological Indices of Boron B12

Some Vertex/Edge-Degree-Based Topological Indices of $r$ -Apex Trees

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On general reduced second Zagreb index of graphs

Abstract: Recently, Furtula et al.

Cited by 6 publications

References 15 publications

Fixed-Order Chemical Trees with Given Segments and Their Maximum Multiplicative Sum Zagreb Index

Fixed-Order Chemical Trees with Given Segments and Their Maximum Multiplicative Sum Zagreb Index

Degree-Based Topological Indices of Boron B12

Some Vertex/Edge-Degree-Based Topological Indices of r -Apex Trees

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Some Vertex/Edge-Degree-Based Topological Indices of $r$ -Apex Trees