Forgotten polynomial and forgotten index of certain interconnection networks

OMA-Vol. 1 (2017), Issue 1, pp. 44–59 | Open Access Full-Text PDF
Hajra Siddiqui, Mohammad Reza Farahani
Abstract: Chemical reaction network theory is an area of applied mathematics that attempts to model the behavior of real world chemical systems. Since its foundation in the 1960s, it has attracted a growing research community, mainly due to its applications in biochemistry and theoretical chemistry. It has also attracted interest from pure mathematicians due to the interesting problems that arise from the mathematical structures involved. It is experimentally proved that many properties of the chemical compounds and their topological indices are correlated. In this report, we compute closed form of forgotten polynomial and forgotten index for interconnection networks. Moreover we give graphs to see dependence of our results on the parameters of structures.
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Integral inequalities for differentiable harmonically \((s,m)\)-preinvex functions

OMA-Vol. 1 (2017), Issue 1, pp. 25–33 | Open Access Full-Text PDF
Imran Abbas Baloch, Imdat İşcan
Abstract: In this paper, we define a new generalized class of preinvex functions which includes harmonically \((s,m)\)-convex functions as a special case and establish a new identity. Using this identity, we introduce some new integral inequalities for harmonically \((s,m)\)-preinvex functions.
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K-Banhatti and K-hyper Banhatti indices of dominating David Derived network

OMA-Vol. 1 (2017), Issue 1, pp. 13–24 | Open Access Full-Text PDF
Wei Gao, Batsha Muzaffar, Waqas Nazeer
Abstract: Let \(G\) be connected graph with vertex \(V(G)\) and edge set \(E(G)\). The first and second \(K\)-Banhatti indices of \(G\) are defined as \(B_{1}(G)=\sum\limits_{ue}[d_{G}(u)+d_{G}(e)]\) and \(B_{2}(G)=\sum\limits_{ue}[d_{G}(u)d_{G}(e)]\) ,where \(ue\) means that the vertex \(u\) and edge \(e\) are incident in \(G\). The first and second \(K\)-hyper Banhatti indices of \(G\) are defined as \(HB_{1}(G)=\sum\limits_{ue}[d_{G}(u)+d_{G}(e)]^{2}\) and \(HB_{2}(G)=\sum\limits_{ue}[d_{G}(u)d_{G}(e)]^{2}\). In this paper, we compute the first and second \(K\)-Banhatti and \(K\)-hyper Banhatti indices of Dominating David Derived networks.
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An implicit viscosity technique of nonexpansive mapping in CAT(0) spaces

OMA-Vol. 1 (2017), Issue 1, pp. 1–12 | Open Access Full-Text PDF
Iftikhar Ahmad, Maqbool Ahmad
Abstract: In this paper, we present a new viscosity technique of nonexpansive mappings in the framework of CAT(0) spaces. The strong convergence theorems of the proposed technique is proved under certain assumptions imposed on the sequence of parameters. The results presented in this paper extend and improve some recent announced in the current literature.
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