Abstract
The first and second Hyper-Zagreb index of a connected graph $G$ is defined by $HM_{1}(G)=\sum_{uv \in E(G)}[d(u)+d(v)]^{2}$ and $HM_{2}(G)=\sum_{uv \in E(G)}[d(u).d(v)]^{2}$. In this paper, the first and second Hyper-Zagreb indices of certain graphs are computed. Also the bounds for the first and second Hyper-Zagreb indices are determined. Further linear regression analysis of the degree based indices with the boiling points of benzenoid hydrocarbons is carried out. The linear model, based on the Hyper-Zagreb index, is better than the models corresponding to the other distance based indices.
Highlights
IntroductionA molecular graph represents the topology of a molecule, by considering how the atoms are connected
In theoretical chemistry, a molecular graph represents the topology of a molecule, by considering how the atoms are connected
The linear model, based on the Hyper-Zagreb index, is better than the models corresponding to the other distance based indices
Summary
A molecular graph represents the topology of a molecule, by considering how the atoms are connected. The Wiener index W (G) of a connected graph G is defined as the sum of the distances between all pairs of vertices of G [32]. The first and second Zagreb indices of a graph G are defined as [13], M1(G) = uv∈E(G)[d(u) + d(v)] and M2(G) = uv∈E(G)[d(u).d(v)]. The first and second Hyper-Zagreb index of a connected graph G [19] is defined by HM1(G) = uv∈E(G)[d(u) + d(v)]2 and HM2(G) = uv∈E(G)[d(u).d(v)]2. The linear model, based on the Hyper-Zagreb index, is better than the models corresponding to the other distance based indices. 2. Computation of first and second Hyper-Zagreb indices of standard graphs (i) For any path Pn with n vertices, HM1(Pn) =.
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