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
Let be a graph with n vertices and m edges. The sum of absolute value of all coefficients of matching polynomial is called Hosoya index. In this paper, we determine 2<sup>nd</sup> to 4<sup>th</sup...Let be a graph with n vertices and m edges. The sum of absolute value of all coefficients of matching polynomial is called Hosoya index. In this paper, we determine 2<sup>nd</sup> to 4<sup>th</sup> minimum Hosoya index of a kind of tetracyclic graph, with m = n +3.展开更多
In this paper we determine all the bipartite graphs with the maximum sum of squares of degrees among the ones with a given number of vertices and edges.
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.
文摘Let be a graph with n vertices and m edges. The sum of absolute value of all coefficients of matching polynomial is called Hosoya index. In this paper, we determine 2<sup>nd</sup> to 4<sup>th</sup> minimum Hosoya index of a kind of tetracyclic graph, with m = n +3.
基金Supported by the National Natural Science Foundation of China(No.11271300)
文摘In this paper we determine all the bipartite graphs with the maximum sum of squares of degrees among the ones with a given number of vertices and edges.
