A formula was proved for computing the zeroth-order general Randic index of a hexagonal system to explore the correlation between the zeroth-order general Randic index and the π-electronic energy of a hexagonal syste...A formula was proved for computing the zeroth-order general Randic index of a hexagonal system to explore the correlation between the zeroth-order general Randic index and the π-electronic energy of a hexagonal system.As a consequence,the extremal hexagonal systems with minimum or maximum zeroth-order general Randic index were completely characterized.Moreover,by using the least-square fit method and regression analysis,a new and close relation was found between the zeroth-order general Randic index and the π-electronic energy of a hexagonal system.So the zeroth-order general Randic index is a good measure of the π-electronic energies for benzenoid hydrocarbons.展开更多
Let G be a connected graph with order n,minimum degree δ = δ（G） and edge-connectivity λ =λ（G）. A graph G is maximally edge-connected if λ = δ, and super edge-connected if every minimum edgecut consists of ed...Let G be a connected graph with order n,minimum degree δ = δ（G） and edge-connectivity λ =λ（G）. A graph G is maximally edge-connected if λ = δ, and super edge-connected if every minimum edgecut consists of edges incident with a vertex of minimum degree. Define the zeroth-order general Randic index R_α-0（G） =Σ x∈V（G） d_G-α（x）, where dG（x） denotes the degree of the vertex x. In this paper, we present two sufficient conditions for graphs and triangle-free graphs to be super edge-connected in terms of the zeroth-order general Randic index for -1 ≤α 〈 0, respectively.展开更多
基金National Natural Science Foundation of China (No. 10901034)Chenguang Program of Shanghai Education Development Foundation,China (No. 2008CG40)
文摘A formula was proved for computing the zeroth-order general Randic index of a hexagonal system to explore the correlation between the zeroth-order general Randic index and the π-electronic energy of a hexagonal system.As a consequence,the extremal hexagonal systems with minimum or maximum zeroth-order general Randic index were completely characterized.Moreover,by using the least-square fit method and regression analysis,a new and close relation was found between the zeroth-order general Randic index and the π-electronic energy of a hexagonal system.So the zeroth-order general Randic index is a good measure of the π-electronic energies for benzenoid hydrocarbons.
基金supported by the National Natural Science Foundation of China(No.11501490,61373019,11371307)by the Natural Science Foundation of Shandong Province(No.ZR2015AM006)
文摘Let G be a connected graph with order n,minimum degree δ = δ（G） and edge-connectivity λ =λ（G）. A graph G is maximally edge-connected if λ = δ, and super edge-connected if every minimum edgecut consists of edges incident with a vertex of minimum degree. Define the zeroth-order general Randic index R_α-0（G） =Σ x∈V（G） d_G-α（x）, where dG（x） denotes the degree of the vertex x. In this paper, we present two sufficient conditions for graphs and triangle-free graphs to be super edge-connected in terms of the zeroth-order general Randic index for -1 ≤α 〈 0, respectively.
