Abstract
AbstractRandom structure plays an important role in the composition of compounds, and topological index is an important index to measure indirectly the properties of compounds. The Zagreb indices and its revised versions (or redefined versions) are frequently used chemical topological indices, which provide the theoretical basis for the determination of various physical-chemical properties of compounds. This article uses the tricks of probability theory to determine the reduced second Zagreb index and hyper-Zagreb index of two kinds of vital random graphs:G(n,p) andG(n,m).
Highlights
The Zagreb index named as the capital of Croatia is one of the first chemical topological indices to be defined
We focus on the following two versions of Zagreb index:
The main contribution of this paper is to study the reduced second Zagreb index and hyper-Zagreb index of G(n, p) and G(n,m)
Summary
The Zagreb index named as the capital of Croatia is one of the first chemical topological indices to be defined. The research on Zagreb index has a long history. It has always been the primary chemical topological index studied by theoretical chemists and has a wide range of applications in various chemical engineering fields. The research on random graphs has penetrated into every field of science, even social sciences. The most famous example is “six degrees of separation”, which is stated that the diameter of social random network graph does not exceed 6.
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