The eccentricity of a vertex in a graph is the maximum distance from the vertex to any other vertex. Two structure topological indices: eccentric connectivity index and connective eccentricity index involving eccentri...The eccentricity of a vertex in a graph is the maximum distance from the vertex to any other vertex. Two structure topological indices: eccentric connectivity index and connective eccentricity index involving eccentricity have a wide range of applications in structure-activity relationships and pharmaceutical drug design etc. In this paper, we investigate the eccentric connectivity index and the connective eccentricity index of a (3, 6)-fullerene. We find a relation between the radius and the number of spokes of a (3, 6)-fullerene. Based on the relation, we give the computing formulas of the eccentric connectivity index and the connective eccentricity index of a (3, 6)-fullerene, respectively.展开更多
The eccentric connectivity index and connective eccentricity index are important topological indices for chemistry. In this paper, we investigate the eccentric connectivity index and connective eccentricity index of b...The eccentric connectivity index and connective eccentricity index are important topological indices for chemistry. In this paper, we investigate the eccentric connectivity index and connective eccentricity index of boron-nitrogen fullerenes, respectively. And we give computing formulas of eccentric connectivity index and connective eccentricity index of all boron-nitrogen fullerenes with regular structure.展开更多
Two nonisomorphic graphs G and H are said to be matching equivalent if and only if G and H have the same matching polynomials. In this paper, some families matching equivalent graphs are constructed. In particular, a ...Two nonisomorphic graphs G and H are said to be matching equivalent if and only if G and H have the same matching polynomials. In this paper, some families matching equivalent graphs are constructed. In particular, a new method to construct cospectral forests is given.展开更多
The Lanzhou index of a graph <em>G</em> is defined as the sum of the product between <img src="Edit_267e1b98-b5dd-40b4-b5f0-c9e5e012d359.bmp" alt="" /> and square of <em>d&l...The Lanzhou index of a graph <em>G</em> is defined as the sum of the product between <img src="Edit_267e1b98-b5dd-40b4-b5f0-c9e5e012d359.bmp" alt="" /> and square of <em>d<sub>u</sub></em> over all vertices <em>u</em> of <em>G</em>, where <em>d<sub>u</sub></em> and <img src="Edit_0cc51468-628a-4a8a-8205-eec1f93624aa.bmp" alt="" /> are respectively the degree of <em>u</em> in <em>G</em> and the degree of <em>u</em> in the complement graph <img src="Edit_2027b773-bcdd-4cbc-b746-bd9b93390798.bmp" alt="" />of <em>G</em>. <em>R</em>(<em>G</em>) is obtained from <em>G</em> by adding a new vertex corresponding to each edge of <em>G</em>, then joining each new vertex to the end vertices of the corresponding edge. Lanzhou index is an important topological index. It is closely related to the forgotten index and first Zagreb index of graphs. In this note, we characterize the bound of Lanzhou index of <em>R</em>(<em>T</em>) of a tree <em>T</em>. And the corresponding extremal graphs are also determined.展开更多
文摘The eccentricity of a vertex in a graph is the maximum distance from the vertex to any other vertex. Two structure topological indices: eccentric connectivity index and connective eccentricity index involving eccentricity have a wide range of applications in structure-activity relationships and pharmaceutical drug design etc. In this paper, we investigate the eccentric connectivity index and the connective eccentricity index of a (3, 6)-fullerene. We find a relation between the radius and the number of spokes of a (3, 6)-fullerene. Based on the relation, we give the computing formulas of the eccentric connectivity index and the connective eccentricity index of a (3, 6)-fullerene, respectively.
文摘The eccentric connectivity index and connective eccentricity index are important topological indices for chemistry. In this paper, we investigate the eccentric connectivity index and connective eccentricity index of boron-nitrogen fullerenes, respectively. And we give computing formulas of eccentric connectivity index and connective eccentricity index of all boron-nitrogen fullerenes with regular structure.
文摘Two nonisomorphic graphs G and H are said to be matching equivalent if and only if G and H have the same matching polynomials. In this paper, some families matching equivalent graphs are constructed. In particular, a new method to construct cospectral forests is given.
文摘The Lanzhou index of a graph <em>G</em> is defined as the sum of the product between <img src="Edit_267e1b98-b5dd-40b4-b5f0-c9e5e012d359.bmp" alt="" /> and square of <em>d<sub>u</sub></em> over all vertices <em>u</em> of <em>G</em>, where <em>d<sub>u</sub></em> and <img src="Edit_0cc51468-628a-4a8a-8205-eec1f93624aa.bmp" alt="" /> are respectively the degree of <em>u</em> in <em>G</em> and the degree of <em>u</em> in the complement graph <img src="Edit_2027b773-bcdd-4cbc-b746-bd9b93390798.bmp" alt="" />of <em>G</em>. <em>R</em>(<em>G</em>) is obtained from <em>G</em> by adding a new vertex corresponding to each edge of <em>G</em>, then joining each new vertex to the end vertices of the corresponding edge. Lanzhou index is an important topological index. It is closely related to the forgotten index and first Zagreb index of graphs. In this note, we characterize the bound of Lanzhou index of <em>R</em>(<em>T</em>) of a tree <em>T</em>. And the corresponding extremal graphs are also determined.
