F index of graphs based on four new operations related to the strong product

Sarala, D.; Deng, Hanyuan; Natarajan, C.; Ayyaswamy, S. K.

doi:10.1016/j.akcej.2018.07.003

Cited by 8 publications

(11 citation statements)

References 14 publications

(23 reference statements)

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“…In this paper, we extend this study and compute FGZI of the Φ-sums graphs (G Φ ⊠ H) under the operation of strong product of Φ(G) and H in term of FGZI of its factor graphs G and H, where Φ ∈ S, R, Q, T { }, G and H are any two connected graphs. e obtained results are general extension of the results of Deng et al [13], Akhter and Imran [14], Liu et al [15] and Sarala et al [16] works. Forthcoming sections are arranged as: Section 2 includes the basic formulae and results, Section 3 covers the main results and Section 4 includes the conclusion.…”

Section: Introductionsupporting

confidence: 87%

“…For more details of aforesaid TIs, see [30,31]. e following graphs are defined with the help of the subdivision related operations (S, R, Q and T), see [16]. obtained.…”

Section: Preliminariesmentioning

confidence: 99%

“…In 1960 Sabidussi introduced the strong product for any two graphs G ∘ H has vertex set Cartesian product V(G) × V(H) such that (s 1 , t 1 ) and (s 2 , t 2 ) will be adjacent in G ∘ H iff: [s 1 � s 2 and t 1 is adjacent to t 2 ] or [t 1 � t 2 and s 1 is adjacent to s 2 ] or [s 1 is adjacent to s 2 and t 1 is adjacent to t 2 ]. Now, the Φ-sum graph under the operation of strong product is defined in [16].…”

Section: Preliminariesmentioning

confidence: 99%

“…Liu et al [15] computed the FGZI of Φ-sum graphs under the operation of Cartesian product. Sarala et al [16] computed the F-index of Φ-sum graphs under the operation of strong product. For further study, we refer to [17][18][19][20][21][22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Computing FGZ Index of Sum Graphs under Strong Product

Peng

Javed

Javaid

et al. 2021

Journal of Mathematics

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Topological index (TI) is a function that assigns a numeric value to a (molecular) graph that predicts its various physical and structural properties. In this paper, we study the sum graphs (S-sum, R-sum, Q-sum and T-sum) using the subdivision related operations and strong product of graphs which create hexagonal chains isomorphic to many chemical compounds. Mainly, the exact values of first general Zagreb index (FGZI) for four sum graphs are obtained. At the end, FGZI of the two particular families of sum graphs are also computed as applications of the main results. Moreover, the dominating role of the FGZI among these sum graphs is also shown using the numerical values and their graphical presentations.

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Section: Introductionsupporting

confidence: 87%

“…For more details of aforesaid TIs, see [30,31]. e following graphs are defined with the help of the subdivision related operations (S, R, Q and T), see [16]. obtained.…”

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Computing FGZ Index of Sum Graphs under Strong Product

Peng

Javed

Javaid

et al. 2021

Journal of Mathematics

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“…Recently, Sarala et al [22] obtained the F-index of the strong product based φ-sum graphs. The theme of this note is to compute FGZI and GRI of φ-sum graphs G +φ constructed by the strong product of graphs φ(G) and…”

Section: Introductionmentioning

confidence: 99%

On bounds for topological descriptors of φ-sum graphs

Chu

Javed

Javaid

et al. 2020

Journal of Taibah University for Science

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The properties of chemical compounds are very important for the studies of the nonisomorphism phenomenon's related to the molecular graphs. Topological indices (TIs) are one of the mathematical tools which are used to study these properties. Gutman and Trinajsti [Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons. Chem Phys Lett. 1972;17(4):535-538] defined the Zagreb indices (descriptors) to find correlation value between a molecular graph and its total π-electron energy. Later on, Bollobás and Erdös [Graphs of extremal weights. Ars Comb; 1998;50:225-233] defined the most general form of these indices (descriptors) called by general Randić index (GRI) and first general Zagreb index (FGZI), respectively. In this paper, we computed the bounds for FGZI and GRI of φ-sum graphs, obtained by the strong product of the graph φ(G) with another graph , where φ(G) is constructed using four subdivision operations on the graph G. At the end, we also include the results for some particular families of graphs as the applications of the obtained results.

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Topological indices of the wreath product of graphs

Zhang

Wang

Brunetti

2022

Discrete Math. Algorithm. Appl.

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Topological indices, i.e., numerical invariants suitably associated to graphs and only depending upon their isomorphism type, have important applications in Chemistry. Their computation constitutes an important branch of Chemical Graph Theory. In this paper, we focus on some degree and distance-based invariants related to the Zagreb indices, the Szeged index and the Wiener index, namely, the F-index, the vertex PI index and the hyper-Wiener index. In particular, we find the formulæ to compute these topological invariants for wreath product of graphs.

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F index of graphs based on four new operations related to the strong product

Abstract: View related articles View Crossmark data Citing articles: 4 View citing articles Please cite this article in press as: D. Sarala, et al., F index of graphs based on four new operations related to the strong product,

Cited by 8 publications

References 14 publications

Computing FGZ Index of Sum Graphs under Strong Product

Computing FGZ Index of Sum Graphs under Strong Product

On bounds for topological descriptors of φ-sum graphs

Topological indices of the wreath product of graphs

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