Scholarlink

<p>The energy <i>En</i>(<i>G</i>) of a graph <i>G</i> is defined as the sum of the absolute values of its eigenvalues. The Hosoya index <i>Z</i>(<i>G</i>) of a graph <i>G</i> is the number of independent edge subsets of <i>G</i>, including the empty set. For any given degree sequence <i>D</i>, we characterize the caterpillar <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {S}(D)\)</EquationSource> </InlineEquation> that has the minimum <i>Z</i> and <i>En</i>. We also show that <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(Z(\mathcal {S}(D))&lt;Z(\mathcal {S}(Y))\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(En(\mathcal {S}(D))&lt;En(\mathcal {S}(Y))\)</EquationSource> </InlineEquation> for any degree sequences <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(Y=(y_1,\dots ,y_n)\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(D=(d_1,\dots ,d_n)\)</EquationSource> </InlineEquation> with <Equation ID="Equ39"> <EquationSource Format="TEX">\(\sum _{i=1}^{n}y_i=\sum _{i=1}^{n}d_i\text { and }\sum _{i=1}^{k}y_i\le \sum _{i=1}^{k}d_i \text { for all }1\le k \le n.\)</EquationSource> </Equation></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

Small energy and Hosoya index among caterpillars with a given degree sequence

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年10月10日

查看全文
  • Eric O. D. Andriantiana,
  • Xhanti Sinoxolo

摘要

The energy En(G) of a graph G is defined as the sum of the absolute values of its eigenvalues. The Hosoya index Z(G) of a graph G is the number of independent edge subsets of G, including the empty set. For any given degree sequence D, we characterize the caterpillar \(\mathcal {S}(D)\) that has the minimum Z and En. We also show that \(Z(\mathcal {S}(D))<Z(\mathcal {S}(Y))\) and \(En(\mathcal {S}(D))<En(\mathcal {S}(Y))\) for any degree sequences \(Y=(y_1,\dots ,y_n)\) and \(D=(d_1,\dots ,d_n)\) with \(\sum _{i=1}^{n}y_i=\sum _{i=1}^{n}d_i\text { and }\sum _{i=1}^{k}y_i\le \sum _{i=1}^{k}d_i \text { for all }1\le k \le n.\)