Very recently D.Vukicevic et al.[8]introduced a new topological index for a molecular graph G named Lanzhou index as∑_(u∈V(G))d_(u)d^(2)_(u),where d_(u)and d_(u)denote the degree of vertex u in G and in its compleme...Very recently D.Vukicevic et al.[8]introduced a new topological index for a molecular graph G named Lanzhou index as∑_(u∈V(G))d_(u)d^(2)_(u),where d_(u)and d_(u)denote the degree of vertex u in G and in its complement respectively.Lanzhou index Lz(G)can be expressed as(n-1)M_(1)(G)-F(G),where M_(1)(G)and F(G)denote the first Zagreb index and the forgotten index of G respectively,and n is the number of vertices in G.It turns out that Lanzhou index outperforms M_(1)(G)and F(G)in predicting the logarithm of the octanol-water partition coefficient for octane and nonane isomers.It was shown that stars and balanced double stars are the minimal and maximal trees for Lanzhou index respectively.In this paper,we determine the unicyclic graphs and the unicyclic chemical graphs with the minimum and maximum Lanzhou indices separately.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
基金Supported by the National Natural Science Foundation of China(11871256)the Chinese-Croatian bilateral project(7-22)。
文摘Very recently D.Vukicevic et al.[8]introduced a new topological index for a molecular graph G named Lanzhou index as∑_(u∈V(G))d_(u)d^(2)_(u),where d_(u)and d_(u)denote the degree of vertex u in G and in its complement respectively.Lanzhou index Lz(G)can be expressed as(n-1)M_(1)(G)-F(G),where M_(1)(G)and F(G)denote the first Zagreb index and the forgotten index of G respectively,and n is the number of vertices in G.It turns out that Lanzhou index outperforms M_(1)(G)and F(G)in predicting the logarithm of the octanol-water partition coefficient for octane and nonane isomers.It was shown that stars and balanced double stars are the minimal and maximal trees for Lanzhou index respectively.In this paper,we determine the unicyclic graphs and the unicyclic chemical graphs with the minimum and maximum Lanzhou indices separately.
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.
基金supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“Research on graph theory problems of topological parameters based on graph matrix spectrum”(2021D01C069)the National Natural Science Foundation of the People’s Republic of China“Research on spectral properties and related issue of graph operations”(12161085)。
