Computing Analysis for First Zagreb Connection Index and Coindex of Resultant Graphs

Ali

et al. 2021

Journal of Chemistry

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Metal-organic networks (MONs) are among the unique complex and porous chemical compounds. So, these chemical compounds consist of metal ions (vertices) and organic ligands (edges between vertices). These networks represent large pore volume, extreme surface area, morphology, excellent chemical stability, highly porous and crystalline materials, and octahedral clusters. MONs are mostly used in assessment of chemicals, gas and energy storage devices, sensing, separation and purification of different gases, heterogeneous catalysis, environmental hazard, toxicology, adsorption analysis, biomedical applications, and biocompatibility. Recently, drug delivery, cancer imaging, and biosensing have been investigated by biomedical applications of zinc-related MONs. The versatile applications of these MONs make them helpful tools in many fields of science in recent decade. In this paper, we discuss the two different zinc oxide and zinc silicate related MONs according to the number of increasing layers of metal and organic ligands together. We also compute the connection-based Zagreb indices such as first Zagreb connection index (ZCI), second ZCI, modified first ZCI, modified second ZCI, modified third ZCI, and modified fourth ZCI. Moreover, a comparison is also included between the zinc-related MONs by using numerical values of connection-based Zagreb indices. Finally, we conclude that zinc silicate-related MON is better than zinc oxide-related MON for all values of n.

Section: Introductionmentioning

confidence: 99%

Comparing Zinc Oxide- and Zinc Silicate-Related Metal-Organic Networks via Connection-Based Zagreb Indices

Hussain

Ali

et al. 2021

Journal of Chemistry

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“…Nilanjan et al calculated F-coindex of some graph operations (see [16]). Javaid et al calculated the first Zagreb connection index and coindex of some derived graphs [17]. Ramane et al calculated coindices for the transmission and reciprocal transmission-based graphs (see [18]).…”

Section: Introductionmentioning

confidence: 99%

Computing Bounds for Second Zagreb Coindex of Sum Graphs

Mathematical Problems in Engineering

Ibraheem

Ahmad

et al. 2021

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Topological indices or coindices are one of the graph-theoretic tools which are widely used to study the different structural and chemical properties of the under study networks or graphs in the subject of computer science and chemistry, respectively. For these investigations, the operations of graphs always played an important role for the study of the complex networks under the various topological indices or coindices. In this paper, we determine bounds for the second Zagreb coindex of a well-known family of graphs called F -sum ( S -sum, R -sum, Q -sum, and T -sum) graphs in the form of Zagreb indices and coindices of their factor graphs, where these graphs are obtained by using four subdivision-related operations and Cartesian product of graphs. At the end, we illustrate the obtained results by providing the exact and bonded values of some specific F -sum graphs.

“…Ramane et al calculated coindices for the transmission-and reciprocal transmission-based graphs (see [16]). Javaid et al computed the first Zagreb connection index and coindex of some derived graphs [17].…”

Section: Introductionmentioning

confidence: 99%

Sharp Bounds of First Zagreb Coindex for $F$ -Sum Graphs

Ibraheem

Ahmad

et al. 2021

Journal of Mathematics

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Let G = V E , E G be a connected graph with vertex set V G and edge set E G . For a graph G, the graphs S(G), R(G), Q(G), and T(G) are obtained by applying the four subdivisions related operations S, R, Q, and T, respectively. Further, for two connected graphs G 1 and G 2 , G 1 + F G 2 are F -sum graphs which are constructed with the help of Cartesian product of F G 1 and G 2 , where F ∈ S , R , Q , T . In this paper, we compute the lower and upper bounds for the first Zagreb coindex of these F -sum (S-sum, R-sum, Q-sum, and T-sum) graphs in the form of the first Zagreb indices and coincides of their basic graphs. At the end, we use linear regression modeling to find the best correlation among the obtained results for the thirteen physicochemical properties of the molecular structures such as boiling point, density, heat capacity at constant pressure, entropy, heat capacity at constant time, enthalpy of vaporization, acentric factor, standard enthalpy of vaporization, enthalpy of formation, octanol-water partition coefficient, standard enthalpy of formation, total surface area, and molar volume.