Akhlaq Ahmad Bhatti

Conserved Quantities in f(R) Gravity via Noether Symmetry

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.

FURTHER INEQUALITIES BETWEEN VERTEX-DEGREE-BASED TOPOLOGICAL INDICES

Topological indices play an important role in mathematical chemistry especially in the quantitative structure–property relationship and quantitative structure–activity relationship studies. Recent research indicates that the augmented Zagreb index (AZI) possess the best correlating ability among several topological indices to predict the certain physico-chemical properties of particular types of molecules. In the present work, several novel bounds (lower and upper) for the AZI in terms of first geometric–arithmetic index, Randić index, atom-bond connectivity index, sum-connectivity index, modified second Zagreb index and harmonic index are established. Moreover, the geometric–arithmetic index and modified second Zagreb index are also among the well known topological indices. Various relations between these two topological indices and some of the aforementioned indices are also derived.

Killing and Noether Symmetries of Plane Symmetric Spacetime

This paper is devoted to investigate the Killing and Noether symmetries of static plane symmetric spacetime. For this purpose, five different cases have been discussed. The Killing and Noether symmetries of Minkowski spacetime in cartesian coordinates are calculated as a special case and it is found that Lie algebra of the Lagrangian is 10 and 17 dimensional respectively. The symmetries of Taub’s universe, anti-deSitter universe, self similar solutions of infinite kind for parallel perfect fluid case and self similar solutions of infinite kind for parallel dust case are also explored. In all the cases, the Noether generators are calculated in the presence of gauge term. All these examples justify the conjecture that Killing symmetries form a subalgebra of Noether symmetries (Bokhari et al. in Int. J. Theor. Phys. 45:1063, 2006).

Bond incident degree (BID) indices of polyomino chains

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. From the derived results, all the results of the papers (An and Xiong, 2016, Deng etźal., 2014, Yarahmadi etźal., 2012) and some results of the papers (Rada, 2014, Ali etźal., 2015) are obtained as corollaries.