Distance Degree Index of Some Derived Graphs

Topological indices are numerical values associated with a graph (structure) that can predict many physical, chemical, and pharmacological properties of organic molecules and chemical compounds. The distance degree (DD) index was introduced by Dobrynin and Kochetova in 1994 for characterizing alkanes by an integer. In this paper, we have determined expressions for a DD index of some derived graphs in terms of the parameters of the parent graph. Specifically, we establish expressions for the DD index of a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph, and paraline graph.

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An Algebraic Approach to Find Some Topological Indices of Derived Graphs of the Benzene Ring

Biointerface Research in Applied Chemistry ◽

10.33263/briac124.54315443 ◽

2021 ◽

Vol 12 (4) ◽

pp. 5431-5443

Keyword(s):

Benzene Ring ◽

Line Graph ◽

Algebraic Approach ◽

Chemical Compounds ◽

Vital Role ◽

Topological Indices ◽

Zagreb Index ◽

Subdivision Graph ◽

Surface Network ◽

P Type

Topological indices play a vital role in understanding the chemical and structural properties of the chemical compounds and nanostructures. By finding the M-polynomial of a graph representing a chemical compound, one can obtain the closed forms of some of the commonly known degree-based topological indices of the compound, such as the Zagreb index, general Randic ́ Index and harmonic index. In this article, we obtain the expression for the M-polynomial of the derived graphs of the Benzene ring embedded in the P-type surface network in 2D, namely the line graph, the subdivision graph, and the line graph of its subdivision. Furthermore, some of the degree-based topological indices are obtained for these graphs using their M-polynomials.

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Hyperbolicity on Graph Operators

Symmetry ◽

10.3390/sym10090360 ◽

2018 ◽

Vol 10 (9) ◽

pp. 360 ◽

Cited By ~ 2

Author(s):

J. Méndez-Bermúdez ◽

Rosalío Reyes ◽

José Rodríguez ◽

José Sigarreta

Keyword(s):

Line Graph ◽

Discrete Mathematics ◽

Total Graph ◽

Subdivision Graph ◽

Gromov Product

A graph operator is a mapping F : Γ → Γ ′ , where Γ and Γ ′ are families of graphs. The different kinds of graph operators are an important topic in Discrete Mathematics and its applications. The symmetry of this operations allows us to prove inequalities relating the hyperbolicity constants of a graph G and its graph operators: line graph, Λ ( G ) ; subdivision graph, S ( G ) ; total graph, T ( G ) ; and the operators R ( G ) and Q ( G ) . In particular, we get relationships such as δ ( G ) ≤ δ ( R ( G ) ) ≤ δ ( G ) + 1 / 2 , δ ( Λ ( G ) ) ≤ δ ( Q ( G ) ) ≤ δ ( Λ ( G ) ) + 1 / 2 , δ ( S ( G ) ) ≤ 2 δ ( R ( G ) ) ≤ δ ( S ( G ) ) + 1 and δ ( R ( G ) ) − 1 / 2 ≤ δ ( Λ ( G ) ) ≤ 5 δ ( R ( G ) ) + 5 / 2 for every graph which is not a tree. Moreover, we also derive some inequalities for the Gromov product and the Gromov product restricted to vertices.

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Reformulated Zagreb Indices of Some Derived Graphs

Mathematics ◽

10.3390/math7040366 ◽

2019 ◽

Vol 7 (4) ◽

pp. 366 ◽

Cited By ~ 6

Author(s):

Jia-Bao Liu ◽

Bahadur Ali ◽

Muhammad Aslam Malik ◽

Hafiz Muhammad Afzal Siddiqui ◽

Muhammad Imran

Keyword(s):

Physical Properties ◽

Chemical Structure ◽

Topological Index ◽

Chemical Reactivity ◽

Line Graph ◽

Total Graph ◽

Zagreb Indices ◽

Subdivision Graph ◽

Chemical Constitution ◽

Vertex Degrees

A topological index is a numeric quantity that is closely related to the chemical constitution to establish the correlation of its chemical structure with chemical reactivity or physical properties. Miličević reformulated the original Zagreb indices in 2004, replacing vertex degrees by edge degrees. In this paper, we established the expressions for the reformulated Zagreb indices of some derived graphs such as a complement, line graph, subdivision graph, edge-semitotal graph, vertex-semitotal graph, total graph, and paraline graph of a graph.

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On Topological Indices of Total Graph and Its Line Graph for Kragujevac Tree Networks

Complexity ◽

10.1155/2021/8695121 ◽

2021 ◽

Vol 2021 ◽

pp. 1-32

Author(s):

Salma Kanwal ◽

Ayesha Riasat ◽

Muhammad Kamran Siddiqui ◽

Shabnam Malik ◽

Khadija Sarwar ◽

...

Keyword(s):

Line Graph ◽

Topological Indices ◽

Total Graph ◽

Tree Networks ◽

Topological Features

Kragujevac tree is indicated by K ; K ∈ K g q = s 2 t + 1 + 1 , s with order and size s 2 t + 1 + 1 and s 2 t + 1 , respectively. In this paper, we have a look at certain topological features of the total graph and line graph of the total graph of the considered tree, i.e ., Kragujevac tree, by computing different topological indices and polynomials.

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On the Degree-Based Topological Indices of Some Derived Networks

Mathematics ◽

10.3390/math7070612 ◽

2019 ◽

Vol 7 (7) ◽

pp. 612 ◽

Cited By ~ 3

Author(s):

Haidar Ali ◽

Muhammad Ahsan Binyamin ◽

Muhammad Kashif Shafiq ◽

Wei Gao

Keyword(s):

Chemical Structure ◽

Chemical Properties ◽

Chemical Compounds ◽

Wiener Index ◽

Topological Indices ◽

Theoretical Chemistry ◽

Zagreb Index ◽

Entire Structure ◽

Physical Chemical ◽

Chemical Descriptors

There are numeric numbers that define chemical descriptors that represent the entire structure of a graph, which contain a basic chemical structure. Of these, the main factors of topological indices are such that they are related to different physical chemical properties of primary chemical compounds. The biological activity of chemical compounds can be constructed by the help of topological indices. In theoretical chemistry, numerous chemical indices have been invented, such as the Zagreb index, the Randić index, the Wiener index, and many more. Hex-derived networks have an assortment of valuable applications in drug store, hardware, and systems administration. In this analysis, we compute the Forgotten index and Balaban index, and reclassified the Zagreb indices, A B C 4 index, and G A 5 index for the third type of hex-derived networks theoretically.

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Topological indices of the subdivision graph and the line graph of subdivision graph of the wheel graph

Journal of Discrete Mathematical Sciences and Cryptography ◽

10.1080/09720529.2021.1892317 ◽

2021 ◽

Vol 24 (2) ◽

pp. 589-601

Author(s):

Melaku Berhe Belay ◽

Chunxiang Wang ◽

Abdul Jalil M. Khalaf ◽

Hamid Hosseini ◽

Mohammad Reza Farahani

Keyword(s):

Line Graph ◽

Topological Indices ◽

Subdivision Graph ◽

Wheel Graph

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ON COMPUTATION OF NEW DEGREE-BASED TOPOLOGICAL INDICES OF SILICATE CHAIN GRAPH

10.37516/global.j.appl.eng.math.2019.0073 ◽

2019 ◽

pp. 14-34

Author(s):

Rachanna Kanabur ◽

S.K. Giregol ◽

Anand Jirli ◽

Iranna M. Chanal

Keyword(s):

Organic Molecules ◽

Topological Indices ◽

Pharmacological Properties ◽

Chain Graph ◽

Physico Chemical ◽

Silicate Chain

The Arithmetic-Geometric index (AG1 index), SK index, SK1 index, SK2 indices of a graph G was introduced by V. S. Shigehalli and R. R. Kanabur. These topological indices explain the modeling of various physico-chemical, biological and pharmacological properties of organic molecules in chemistry and explains studies of various results on Silicate Chain Graph.

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Induced cycle path number of derived graphs

Discrete Mathematics Algorithms and Applications ◽

10.1142/s179383091650066x ◽

2016 ◽

Vol 08 (04) ◽

pp. 1650066

Author(s):

J. Paulraj Joseph ◽

S. Rosalin

Keyword(s):

Line Graph ◽

Block Graph ◽

Minimum Order ◽

Total Graph ◽

Power Graph ◽

Subdivision Graph ◽

Path Partition ◽

Simple Connected Graph ◽

Path Number ◽

Cycle Path

An induced cycle path partition of a simple connected graph [Formula: see text] is a partition of [Formula: see text] into subsets such that the subsets induce cycles and paths. The minimum order taken over all induced cycle path partitions is called the induced cycle path number of [Formula: see text] and is denoted by [Formula: see text]. In this paper, we investigate the induced cycle path number of some derived graphs such as line graph, block graph, subdivision graph, power graph and total graph.

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On Analysis of Banhatti Indices for Hyaluronic Acid Curcumin and Hydroxychloroquine

Journal of Chemistry ◽

10.1155/2021/7468857 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Wenhu Wang ◽

Muhammad Naeem ◽

Abdul Rauf ◽

Ayesha Riasat ◽

Adnan Aslam ◽

...

Keyword(s):

Hyaluronic Acid ◽

Chemical Properties ◽

Topological Indices ◽

Graph Structure ◽

Harmonic Index ◽

Physical Chemical ◽

Explicit Expressions

Topological indices are numerical numbers assigned to the graph/structure and are useful to predict certain physical/chemical properties. In this paper, we give explicit expressions of novel Banhatti indices, namely, first K Banhatti index B 1 G , second K Banhatti index B 2 G , first K hyper-Banhatti index HB 1 G , second K hyper-Banhatti index HB 2 G , and K Banhatti harmonic index H b G for hyaluronic acid curcumin and hydroxychloroquine. The multiplicative version of these indices is also computed for these structures.

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