The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, whe...The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, where d( u ) denotes the degree of a vertex u in G. The paper mainly provides the upper and lower bounds of the exponential Randić index in quasi-tree graphs, and characterizes the extremal graphs when the bounds are achieved.展开更多
Randićenergy was first defined in the paper [1]. Using minimum covering set, we have introduced the minimum covering Randićenergy RE<sub>C</sub> (G) of a graph G in this paper. This p...Randićenergy was first defined in the paper [1]. Using minimum covering set, we have introduced the minimum covering Randićenergy RE<sub>C</sub> (G) of a graph G in this paper. This paper contains computation of minimum covering Randićenergies for some standard graphs like star graph, complete graph, thorn graph of complete graph, crown graph, complete bipartite graph, cocktail graph and friendship graphs. At the end of this paper, upper and lower bounds for minimum covering Randićenergy are also presented.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
文摘The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, where d( u ) denotes the degree of a vertex u in G. The paper mainly provides the upper and lower bounds of the exponential Randić index in quasi-tree graphs, and characterizes the extremal graphs when the bounds are achieved.
基金The project supported by the Science and Technology Foundation of Education Department ofFujian(JA08266)the Research Foundation of Ningde Teachers College(2008102)
文摘Randićenergy was first defined in the paper [1]. Using minimum covering set, we have introduced the minimum covering Randićenergy RE<sub>C</sub> (G) of a graph G in this paper. This paper contains computation of minimum covering Randićenergies for some standard graphs like star graph, complete graph, thorn graph of complete graph, crown graph, complete bipartite graph, cocktail graph and friendship graphs. At the end of this paper, upper and lower bounds for minimum covering Randićenergy are also presented.
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.
