On the Lanzhou Indices of Trees under Graph Decoration

• 作者: Xiaolin Zeng Tingzeng Wu
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Lanzhou Index Zagreb Index Forgotten Index Graph Operator
• 年，卷（期）: 2021,（2）
• 页码范围: 85-90
• 页数: 6页
• 分类号: O15

摘要

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_u</em> over all vertices <em>u</em> of <em>G</em>, where <em>d_u</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.