Scholarlink

<p>The transmission of a vertex <i>v</i> in a (chemical) graph <i>G</i> is the sum of distances from <i>v</i> to other vertices in <i>G</i>. If any two vertices of <i>G</i> have different transmissions, then <i>G</i> is transmission irregular. The Wiener index <i>W</i>(<i>G</i>) of a graph <i>G</i> is the sum of all distances between all unordered pairs of vertices in <i>G</i>, which has another formula as the half of the sum of transmissions of all vertices of <i>G</i>. In this paper, we consider the Wiener index maximization problem on the set of transmission irregular trees of a given order <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n \in {\mathbb {N}}\)</EquationSource> </InlineEquation>. We solve the problem for all odd values of <i>n</i> and for almost all even values of <i>n</i>. Each resolved extremal problem has a unique solution that is a chemical tree.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On the transmission irregular trees with the maximum Wiener index

  • 期刊论文

  • 发表日期：

    2026年1月11日

查看全文
  • Ivan Damnjanović,
  • Anran Xu,
  • Kexiang Xu

摘要

The transmission of a vertex v in a (chemical) graph G is the sum of distances from v to other vertices in G. If any two vertices of G have different transmissions, then G is transmission irregular. The Wiener index W(G) of a graph G is the sum of all distances between all unordered pairs of vertices in G, which has another formula as the half of the sum of transmissions of all vertices of G. In this paper, we consider the Wiener index maximization problem on the set of transmission irregular trees of a given order \(n \in {\mathbb {N}}\) . We solve the problem for all odd values of n and for almost all even values of n. Each resolved extremal problem has a unique solution that is a chemical tree.