Computing First Zagreb index and F-index of New C-products of Graphs

Basavanagoud, B.; Gao, Wei; Patil, Shreekant; Desai, Veena R.; Mirajkar, Keerthi G.; Pooja, B

doi:10.21042/amns.2017.1.00024

Cited by 23 publications

(19 citation statements)

References 24 publications

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“…The edge set E(TSM) is divided into eighteen edge partitions based on the degree of end vertices. The edge partition E u,v (TSM) contains m u,v edges uv, where S u = u, S v = v, and (16,20) 4 (16,28) 4 (19,20) 4 (19,29) 4 (19,32) 4 (20,20) 2m + 2n − 20 (20,28) 4 (20,32) 4m + 4n − 36 (28,32) 4 (29,32) 4 (29,36) 2 (32,32) 2m + 2n − 18 (32,36) 4m + 4n − 36 (36,36) 3mn Table 3. The fourth atom-bond connectivity index ABC 4 is defined as: Table 3.…”

Section: Methodsmentioning

confidence: 99%

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On the Degree-Based Topological Indices of the Tickysim SpiNNaker Model

Imran

Siddiqui

Ahmad

et al. 2018

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Tickysim is a clock tick-based simulator for the inter-chip interconnection network of the SpiNNaker architecture. Network devices such as arbiters, routers, and packet generators store, read, and write forward data through fixed-length FIFO buffers. At each clock tick, every component executes a “read” phase followed by a “write” phase. The structures of any finite graph which represents numerical quantities are known as topological indices. In this paper, we compute degree-based topological indices of the Tickysim SpiNNaker Model ( T S M ) sheet.

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Section: Methodsmentioning

confidence: 99%

“…Some different utilizations of the atomic descriptors of sub-atomic diagrams and systems are given in the reference list and the references [33]. These applications and writing survey inspired us to investigate some new substance diagrams and process their topological indices [34][35][36][37].…”

Section: Applications Of Topological Indicesmentioning

confidence: 99%

On the Degree-Based Topological Indices of the Tickysim SpiNNaker Model

Imran

Siddiqui

Ahmad

et al. 2018

Axioms

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“…For details about topological indices and its applications we refer [15][16][17][18][19][20][21][22].…”

Section: Basic Definitionsmentioning

confidence: 99%

Zagreb Polynomials and Redefined Zagreb Indices of Silicon-Carbon Si2C3-I[p,q] and Si2C3-II[p,q]

Kwun¹,

Virk²,

Nazeer³

et al. 2018

Preprint

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The application of graph theory in chemical and molecular structure research far exceeds people's expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonded by edges. In this report, we study the silicon-carbon Si2C3-I[p,q] and Si2C3-II[p,q]. We compute several Zagreb polynomials and Redefined Zagreb indices of these silicon-carbons.

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“…Moreover, TIs are presented into useful identity in the study of the quantitative structure activity relationships (QSARs) and quantitative structure property relationships (QSPRs), which connect the molecular graphs to their biological behaviour [11][12][13][14][15][16]. Mathematically, we represent this link as T � χ(U), where χ is the real-valued function, U is the molecular structure, and T is a real value that depends upon U.…”

Section: Introductionmentioning

confidence: 99%

Zagreb Connection Indices of Subdivision and Semi-Total Point Operations on Graphs

Tang

Ali

Javaid

et al. 2019

Journal of Chemistry

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Representation or coding of the molecular graphs with the help of numerical numbers plays a vital role in the studies of physicochemical and structural properties of the chemical compounds that are involved in the molecular graphs. For the first time, the modified first Zagreb connection index appeared in the paper by Gutman and Trinajstic (1972) to compute total electron energy of the alternant hydrocarbons, but after that, for a long time, it has not been studied. Recently, Ali and Trinajstic (2018) restudied the first Zagreb connection index ZC1, the second Zagreb connection index ZC2, and the modified first Zagreb connection index ZC1∗ to find entropy and acentric factor of the octane isomers. They also reported that the values provided by the International Academy of Mathematical Chemistry show better chemical capability of the Zagreb connection indices than the ordinary Zagreb indices. Assume that S1 and S2 denote the operations of subdivision and semitotal point, respectively. Then, the S-sum graphs Q1+QS2 are obtained by the cartesian product of SQ1 and Q2, where S∈S1,S2, Q1andQ2 are any connected graphs, and SQ1 is a graph obtained after applying the operation S on Q1. In this paper, we compute the Zagreb connection indices (ZC1, ZC2, and ZC1∗) of the S-sum graphs in terms of various topological indices of their factor graphs. At the end, as an application of the computed results, the Zagreb connection indices of the S-sum graphs obtained by the particular classes of alkanes are also included.

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Computing First Zagreb index and F-index of New C-products of Graphs

Cited by 23 publications

References 24 publications

On the Degree-Based Topological Indices of the Tickysim SpiNNaker Model

On the Degree-Based Topological Indices of the Tickysim SpiNNaker Model

Zagreb Polynomials and Redefined Zagreb Indices of Silicon-Carbon <em>Si</em><sub>2</sub><em>C</em><sub>3</sub><em>-I</em>[<em>p,q</em>] and <em>Si</em><sub>2</sub><em>C</em><sub>3</sub><em>-II</em>[<em>p,q</em>]

Zagreb Connection Indices of Subdivision and Semi-Total Point Operations on Graphs

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