Zagreb indices of generalized transformation graphs and their complements

Basavanagoud, B.; Gutman, Ivan; Desai, Veena R.

doi:10.5937/kgjsci1537099b

Cited by 10 publications

(5 citation statements)

References 13 publications

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“…The Table 3 is given by us which gives operator to derive geometric-arithmetic index from M-polynomial. In this section , we obtain M-polynomial of generalized semitotal point graph [5].…”

Section: Notationmentioning

confidence: 99%

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M-Polynomial of Generalized Transformation Graphs B. Basavanagoud and Goutam Veerapur

2020

Electronic Journal of Mathematical Analysis and Applications

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In this paper, we show geomertric-arithmetic index (GA) can be obtained from the M-polynomial of a graph by giving a suitable operator and obtain M-polynomial of generalized transformation graph G and their complements. Furthermore, we derive some degree-based topological indices from the obtained polynomials. The topological indices play an important role in determining physico-chemical properties of chemical graphs and topological indices such as the Randic index, geomertric-arithmetic index are used to predict the bioactivity of chemical compounds, among them the degree-based topological indices can be easily driven from an algebraic expression corresponding to the chemical graphs called M-polynomial.[21] D. Vukičević, B. Furtula, Topological index based on the ratio of geometrical and arithmetical means of end-vertex degrees of edges,

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“…The Table 3 is given by us which gives operator to derive geometric-arithmetic index from M-polynomial. In this section , we obtain M-polynomial of generalized semitotal point graph [5].…”

Section: Notationmentioning

confidence: 99%

“…The generalized transformation graph G xy , introduced by Basavanagoud et al [5] is a graph whose vertex set is V (G) ∪ E(G) and α, β ∈ V (G xy ). The vertices α and β are adjacent in G xy if and only if (a) and (b) holds:…”

Section: Introductionmentioning

confidence: 99%

M-Polynomial of Generalized Transformation Graphs B. Basavanagoud and Goutam Veerapur

2020

Electronic Journal of Mathematical Analysis and Applications

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“…Works pertaining to structure-descriptors of the transformation graphs have been carried out [22,23]. In the present paper, exact expressions for the first and second Hyper-Zagreb indices of the total transformation graphs are determined.…”

Section: Introductionmentioning

confidence: 99%

On Transformed Graphs

Sarkar

Nanjappa

Gutman

2023

Preprint

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The network systems and graphical analysis through the study ofstructural characteristics is a vast field of growing importance inresearch. Topological indices have a significant and crucial role inthe study of structure–property relationships. In this paper, weexamine constructional transformed networks constructed by unique vertex-edge incidence and mutual adjacency associations. Expres-sions for the first and second hyper Zagreb indices and co-indices of these transformed networks and their complements are obtained. MSC Classification: 05C09 , 05C90 , 05C92

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“…The generalized transformation graph G xy introduced recently by Basavanagoud et al [1]., is a graph whose vertex set is…”

Section: Introductionmentioning

confidence: 99%

“…Lemma 1.1. [1] Let G be a graph with n vertices and m edges , Let u ∈ V (G) and e ∈ E(G) then the degree of point and line vertices in G xy are, (i)…”

Section: Introductionmentioning

confidence: 99%

K-Banhatti Indices, K-Hyper Banhatti Indices, Forgotten Index, First Hyper Zagreb Index of Generalized Transformation Graphs Harisha, RANJINI.P.S and V. Lokesha

2021

Electronic Journal of Mathematical Analysis and Applications

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Let G be a simple connected graph. The K-Banhatti indices and K-Hyper Banhatti indices are introduced by Kulli in 2016. The Zagreb indices were introduced in 1972. In this paper, we established the expressions for the K-Banhatti indices, K-Hyper Banhatti indices, Zagreb indices, first Hyper Zagreb indices and Forgotten index of the generalized transformation graphs G xy and their complement graphs are obtained in terms of some parameters of a graph.

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Zagreb indices of generalized transformation graphs and their complements

Abstract: We consider the generalized transformation graphs G ab and obtain expressions for their first and second Zagreb indices and coindices. Analogous expressions are obtained also for the complements of G ab .

Cited by 10 publications

References 13 publications

M-Polynomial of Generalized Transformation Graphs B. Basavanagoud and Goutam Veerapur

M-Polynomial of Generalized Transformation Graphs B. Basavanagoud and Goutam Veerapur

On Transformed Graphs

K-Banhatti Indices, K-Hyper Banhatti Indices, Forgotten Index, First Hyper Zagreb Index of Generalized Transformation Graphs Harisha, RANJINI.P.S and V. Lokesha

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