Abstract
The Lanzhou index of a graph G is defined as the sum of the product between and square of du over all vertices u of G, where du and are respectively the degree of u in G and the degree of u in the complement graph of G. R(G) is obtained from G by adding a new vertex corresponding to each edge of G, 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 R(T) of a tree T. And the corresponding extremal graphs are also determined.
Highlights
We use G to denote a simple graph with vertex set V (G) = {v1, v2, vn} and edge set E (G) = {e1, e2, em}
The Lanzhou index of a graph G is defined as the sum of the product between du and square of du over all vertices u of G, where du and du are respectively the degree of u in G and the degree of u in the complement graph
It is closely related to the forgotten index and first Zagreb index of graphs
Summary
The Lanzhou index of a graph G is defined as the sum of the product between du and square of du over all vertices u of G, where du and du are respectively the degree of u in G and the degree of u in the complement graph We characterize the bound of Lanzhou index of R (T ) of a tree T. The complement graph G of G has the same vertex set V (G) , and two vertices are adjacent in G if and only if they are not adjacent in G.
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