The Zeroth General Randic Index And The Sum-connectivity Index Of Some Graphs

Let G be a simple connected graph and a be an any given real number. The zeroth-order general Randic index expression of0Rα (G) is defined as: Rα(G)=ΣuveE(G)[d(u)d(v)]α, where dG(v) denotes the degree of the vertex v ofG. The Randic index is an important index in molecular topology. There is a good correlation between R of a graph of a substance’s molecular structure with its physical and chemical properties. These properties include the boiling point of water solubility, surface area, etc. Based on such situation, it gives sharp bounds of the zeroth-order Randic index0Rα (G) of all tricyclic graphs with n vertices and k pendent vertices,where α≠0,1.In the connected graph ofG, The zeroth-order general sum-connectivity index expression of0Rα(G) is defined asχα(G)=ΣuveE(du+dv)α (a≠0), where a be an any given real number, dG (v) denotes the degree of the vertex v of G. M.Randic and many scholars discuss the π-electronic energies Eπ of Benzene hydrocarbon, gas-chromatographic retention indices of alkanes RI, and boiling points of aliphatic alcohols BP, and the linear relationship between R(G) and X(G). So, the sum-connectivity index and Randic index have very close connection.