Forgotten Topological Index and Hyper-Zagreb Index of Generalized Transformation Graphs

Basavanagoud, B.; Desai, Veena R.

doi:10.18052/www.scipress.com/bmsa.14.1

Cited by 6 publications

(4 citation statements)

References 9 publications

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“…M (α) 1 for α = 3 can be found already in the paper [1], but neither in the 1970s nor in next 40 years did it attract any attention. Only in 2015, some of its unusual features (in quantitative structure-property chemical applications) have been recognized [54], after which this structure-descriptor suddenly became attractive to mathematical chemists [55][56][57][58][59][60][61][62][63][64][65][66][67][68]. This graph invariant was named forgotten topological index or F-index.…”

Section: Special Casesmentioning

confidence: 99%

Beyond the Zagreb indices

Gutman

Milovanovic²,

Milovanovic³

2020

AKCE International Journal of Graphs and Combinatorics

106

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The two Zagreb indices M 1 = ∑ v d(v) 2 and M 2 = ∑ uv d(u) d(v) are vertex-degree-based graph invariants that have been introduced in the 1970s and extensively studied ever since. In the last few years, a variety of modifications of M 1 and M 2 were put forward. The present survey of these modified Zagreb indices outlines their main mathematical properties, and provides an exhaustive bibliography.

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Section: Special Casesmentioning

confidence: 99%

Beyond the Zagreb indices

Gutman

Milovanovic²,

Milovanovic³

2020

AKCE International Journal of Graphs and Combinatorics

106

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“…Where r∽s ∈ H 2 presents the xy is an edge in H 2 [26]. For the D-sum graphs, refer Figures 1 and 2.…”

Section: (I) S(h) Is a Graph Formed By Inserting A New Vertex In Each Edge Of H (Ii) R(h) Is A Graph Obtained From S(h) By Adding An Edgementioning

confidence: 99%

“…Havare et al computed the F-index and F-coindex for carbon base nanomaterial [25]. Basavanagoud and Desai calculated the F-index and hyper-Zagreb index of generalized transformation graphs [26]. Gao et al calculated electron energy of molecular structures F-index [27].…”

Section: Introductionmentioning

confidence: 99%

Forgotten Coindex for the Derived Sum Graphs under Cartesian Product

Ibraheem¹,

Aljohani²,

Javaid³

et al. 2021

Journal of Chemistry

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A topological index (TI) is a molecular descriptor that is applied on a chemical structure to compute the associated numerical value which measures volume, density, boiling point, melting point, surface tension, or solubility of this structure. It is an efficient mathematical method in avoiding laboratory experiments and time-consuming. The forgotten coindex of a structure or (molecular) graph H is defined as the sum of the degrees of all the possible pairs of nonadjacent vertices in H . For D ∈ S , R , Q , T and the connected graph H , the derived graphs D H are obtained by applying the operations S (subdivided), R (triangle parallel), Q (line superposition), and T (total graph), respectively. Moreover, a derived sum graph ( D -sum graph) is obtained by the Cartesian product of the graph H 2 with the graph D H 1 . In this study, we compute forgotten coindex of the D -sum graphs H 1 + S H 2 ( S -sum), H 1 + R H 2 ( R -sum), H 1 + Q H 2 ( Q -sum), and H 1 + T H 2 ( T -sum) in the form of various indices and coindices of the factor graphs H 1 and H 2 . At the end, we have analyzed our results using numerical tables and graphical behaviour for some particular D -sum graphs.

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“…For different recent study of -index and its co-index, we refer to [8,16,17]. In order to know more about Zagreb polynomials and its co-polynomials for various transformation graphs see [15,18,19].…”

Section: Introductionmentioning

confidence: 99%

Computing F-index, coindex and Zagreb polynomials of the kth generalized transformation graphs

Maji

Ghorai

2020

Heliyon

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In chemical graph theory, forgotten topological index or F -index plays a crucial role to collect information about the properties of chemical compounds. The k th generalized transformation graphs of a molecular graph preserve the entire information on the molecular topology contained in the relevant molecular graph. In this paper, some exact expressions of the F-index and its co-index for the k th generalized transformation graphs are obtained. Also, the Zagreb polynomials, Zagreb co-polynomials and their complements are computed.

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Forgotten Topological Index and Hyper-Zagreb Index of Generalized Transformation Graphs

Abstract: In this paper, we obtain the expressions for forgotten topological index, hyper-Zagreb index and coindex for generalized transformation graphs Gaband their complements \overline/Gab.

Cited by 6 publications

References 9 publications

Beyond the Zagreb indices

Beyond the Zagreb indices

Forgotten Coindex for the Derived Sum Graphs under Cartesian Product

Computing F-index, coindex and Zagreb polynomials of the kth generalized transformation graphs

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