We investigate 𝑓 (𝑅) gravity using the Noether symmetry approach. For this purpose, we consider Friedmann Robertson-Walker (FRW) universe and spherically symmetric spacetimes. The Noether symmetry generators are evaluated for some specific choice of 𝑓 (𝑅) models in the presence of the gauge term. Further, we calculate the corresponding conserved quantities in each case. Moreover, the importance and stability criteria of these models are discussed.

A C 1 piecewise rational trigonometric cubic function with four shape parameters has been constructed to address the problem of visualizing positive data. Simple data-dependent constraints on shape parameters are derived to preserve positivity and assure smoothness. The method is then extended to positive surface data by rational trigonometric bicubic function. The order of approximation of developed interpolant is O h 3 i. 2 2h i δ 2 i,j F xy i,j 1 α i,j − α i,j 1 0 if α i,j α i,j 1 ,

Abstract. This work is devoted to establish a general expression for calculating the bond incident degree (BID) indices of polyomino chains and to characterize the extremal polyomino chains with respect to several well known BID indices.

Numerous molecular structure descriptors, which may be used in theoretical chemistry, are the bond incident degree (BID) indices. This study is devoted to establish a general expression for calculating the BID indices of pentagonal chains and to find the extremal (maximal and minimal) values for a variety of BID indices over the certain collection of pentagonal chains with a fixed number of pentagons.

It is well known fact that several physicochemical properties of chemical compounds are closely related to their molecular structure. Mathematical chemistry provides a method to predict the aforementioned properties of compounds using topological indices. The Zagreb indices are among the most studied topological indices. Recently, three modified versions of the Zagreb indices were proposed independently in [Ali, A.; Trinajstić, N. A novel/old modification of the first Zagreb index, arXiv:1705.10430 [math.CO] 2017; Mol. Inform. 2018, 37, 1800008] and [Naji, A. M.; Soner, N. D.; Gutman, I. On leap Zagreb indices of graphs, Commun. Comb. Optim. 2017, 2, 99–117], which were named as the Zagreb connection indices and the leap Zagreb indices, respectively. In this paper, we check the chemical applicability of the newly considered Zagreb connection indices on the set of octane isomers and establish general expressions for calculating these indices of two well-known dendrimer nanostars.

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(2020) Extremal trees for the modified first Zagreb connection index with fixed number of segments or vertices of degree 2,

The first geometric-arithmetic (GA) index and atom-bond connectivity (ABC) index are molecular structure descriptors which play a significant role in quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies. Das and Trinajstić [Chem. Phys. Lett. 497 (2010) 149-151] showed that GA index is greater than ABC index for all those graphs (except K1,4 and T * , see Figure 1) in which the difference between maximum and minimum degree is less than or equal to 3. In this note, it is proved that GA index is greater than ABC index for line graphs of molecular graphs, for general graphs in which the difference between maximum and minimum degree is less than or equal to (2δ − 1) 2 (where δ is the minimum degree and δ ≥ 2) and for some families of trees. Therefore, a partial solution to an open problem proposed by Das and Trinajstić is given. , 2010 Mathematics Subject Classification. 05C07, 05C35, 92E10. Key words and phrases. first geometric-arithmetic index, atom-bond connectivity index, minimum and maximum degree of a graph, line graph.