F-index of graphs based on four operations related to the lexicographic product

De, Nilanjan

doi:10.26637/mjm0802/0013

Cited by 3 publications

(3 citation statements)

References 20 publications

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“…Moreover, Sarala et al [26], De [27], Pattabiraman et al [28,29], and Suresh et al [30] computed first, second, forgotten, and hyper-and reformulated Zagreb indices for the total sum (T 1 -sum) graph, respectively, where the T 1 -sum graph is obtained with the help of the total operation and lexicographic product of graphs.…”

Section: Introductionmentioning

confidence: 99%

Computing Correlation among the Graphs under Lexicographic Product via Zagreb Indices

Javaid

Javed

Alanazi

et al. 2021

Journal of Chemistry

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A topological index (TI) is a numerical descriptor of a molecule structure or graph that predicts its different physical, biological, and chemical properties in a theoretical way avoiding the difficult and costly procedures of chemical labs. In this paper, for two connected (molecular) graphs G 1 and G 2 , we define the generalized total-sum graph consisting of various (molecular) polygonal chains by the lexicographic product of the graphs T k G 1 and G 2 , where T k G 1 is obtained by applying the generalized total operation T k on G 1 with k ≥ 1 as some integral value. Moreover, we compute the different degree-based TIs such as first Zagreb, second Zagreb, forgotten Zagreb, and hyper-Zagreb. In the end, a comparison among all the aforesaid TIs is also conducted with the help of certain statistical tools for some particular families of generalized total-sum graphs under lexicographic product.

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Section: Introductionmentioning

confidence: 99%

Computing Correlation among the Graphs under Lexicographic Product via Zagreb Indices

Javaid

Javed

Alanazi

et al. 2021

Journal of Chemistry

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“…Sarala et al [21], De [22], Pattabiraman [23], Pattabiraman and Santhakumar [24], and Suresh and Devi [25] have computed different degree-related Zagreb indices for the graphs based online superposition operation and lexicographic product.…”

Section: Introductionmentioning

confidence: 99%

Comparative Study of Generalized Sum Graphs via Degree‐Based Topological Indices

Javaid

Javed

Bonyah³

2022

Journal of Mathematics

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In theoretical chemistry, topological indices (TIs) have important role to predict various physical and structural properties of the study under molecular graphs. Among all topological indices, Zagreb-type indices have been used more effectively in the chemical literature. In this paper, we have computed first Zagreb, second Zagreb, forgotten, and hyper Zagreb indices of the generalized Q -sum graph H 1 Q α H 2 in the form of different TIs of its basic graphs, where α ≥ 1 is a positive integer. This family of graphs is obtained by the lexicographic product of the graph Q α H 1 and H 2 , where Q α H 1 is constructed with the help of the generalized line superposition operation Q α on H 1 . As a conclusion, we also checked the correlation between predefined graph H 1 H 2 under the operation of lexicographic product H 1 and H 2 with newly defined generalized Q -sum graphs H 1 Q α H 2 using linear regression models of various degree-based TIs.

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“…We refer our reader to [9,10,11,12,13,14] for some recent study and application of this index. The hyper Zagreb index, was introduced by Shirrdel et al in [15] and is defined as…”

Section: Introductionmentioning

confidence: 99%

The Forgotten Topological Index of Graphs Based on New Operations Related to the Join of Graphs

Sarkar

Pal

2018

Harmony Search and Nature Inspired Optimization Algorithms

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F-index of graphs based on four operations related to the lexicographic product

Cited by 3 publications

References 20 publications

Computing Correlation among the Graphs under Lexicographic Product via Zagreb Indices

Computing Correlation among the Graphs under Lexicographic Product via Zagreb Indices

Comparative Study of Generalized Sum Graphs via Degree‐Based Topological Indices

The Forgotten Topological Index of Graphs Based on New Operations Related to the Join of Graphs

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