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Let G=(E(G),V(G)) be a (molecular) graph with vertex set V(G) and edge set E(G). The forgotten Zagreb index and the hyper Zagreb index of G are defined by F(G)=∑u∈V(G)d(u)3 and HM(G)=∑uv∈E(G)(d(u)+d(v))2 where d(u) and d(v) are the degrees of the vertices u and v in G, respectively. A recent problem called the inverse problem deals with the numerical realizations of topological indices. We see that there exist trees for all even positive integers with F(G)>88 and with HM(G)>158. Along with the result, we show that there exist no trees with F(G)<90 and HM(G)<160 with some exceptional even positive integers and hence characterize the forgotten Zagreb index and the hyper Zagreb index for trees. [ABSTRACT FROM AUTHOR]

Butane derivatives are chemical compounds formally derived from Butane C4H10 by replacement of one or more hydrogen atoms with other atoms or functional groups. In this paper, we do the QSPR analysis of few Butane derivatives with respect to some selected degree based topological indices and one eccentricity based topological index. In QSPR studies, topological indices are extensively used in determining specific bioactivity of chemical compounds. Our study showcases some important results on the correlation between Heavy atomic count, Complexity, Density, Surface tension and Index of refraction of Butane derivatives with the selected topological indices which further helps in characterizing the predicting power of these topological indices. [ABSTRACT FROM AUTHOR]

The QSPR analysis provides a significant structural insight into the physiochemical properties of butane derivatives. We study some physiochemical properties of fourteen butane derivatives and develop a QSPR model using four topological indices and butane derivatives. Here we analyze how closely the topological indices are related to the physiochemical properties of butane derivatives. For this we compute analytically the topological indices of butane derivatives and plot the graphs between each of these topological indices to the properties of butane derivatives using Origin. This QSPR model exhibits a close correlation between Heavy atomic count, Complexity, Hydrogen bond acceptor count, and Surface tension of butane derivatives with the Redefined first Zagreb index, the Redefined third Zagreb index, the Sum connectivity index and the Reformulated first Zagreb index, respectively. [ABSTRACT FROM AUTHOR]