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Kirchhoff index, multiplicative degree‐Kirchhoff index and spanning trees of the linear crossed hexagonal chains

机译:Kirchhoff指数,乘法程度 - kirchhoff指数和线性交叉六角形链的跨越树

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Abstract > Let H <sub> n </sub> be a linear crossed hexagonal chain with n crossed hexagonals. In this article, we find that the Laplacian (resp. normalized Laplacian) spectrum of H <sub> n </sub> consists of the eigenvalues of a symmetric tridiagonal matrix of order 2 n ?+?1 and a diagonal matrix of order 2 n ?+?1. Based on the properties of these matrices, significant closed formulas for the Kirchhoff index, multiplicative degree‐Kirchhoff index and the number of spanning trees of H <sub> n </sub> are derived. Finally, we show that the Kirchhoff (resp. multiplicative degree‐Kirchhoff) index of H <sub> n </sub> is approximately one quarter of its Wiener (resp. Gutman) index. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译:</span><抽象类型= “主要” 的xml:郎= “EN”> <标题类型= “主”>抽象</ TITLE> >让的 H ^ </ i>的<子> 名词</ I > </子>与名词</ i>的交叉hexagonals线性交叉六边形链。在本文中,我们发现,对拉普拉斯算子(分别地,归一化拉普拉斯)的 H ^ </ i>的<子> 名词</ i>的</子>的频谱由的的对称三对角矩阵的特征值的顺序2 名词</ i>的?+?1和2阶对角矩阵名词</ i>的?+?1。基于这些矩阵的性质,对于基尔霍夫指数,乘法度基尔霍夫指数和跨越的 H ^ </ i>的<子> 名词</ i>的</子树的数目显著闭合式>推导。最后,我们表明,基尔霍夫(相应地乘法度基尔霍夫)的指数的 H ^ </ i>的<子> 名词</ i>的</子>约为其维纳(分别的四分之一。古特曼)指数。 </ p> </ abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-21753/'>《International Journal of Quantum Chemistry》</a> <b style="margin: 0 2px;">|</b><span>2018年第24期</span><b style="margin: 0 2px;">|</b><span>共15页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Pan Yingui&option=202" target="_blank" rel="nofollow">Pan Yingui;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Li Jianping&option=202" target="_blank" rel="nofollow">Li Jianping;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>College of Liberal Arts and SciencesNational University of Defense TechnologyChangsha Hunan China;</p> <p>College of Liberal Arts and SciencesNational University of Defense TechnologyChangsha Hunan China;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/1186.html" title="物理化学(理论化学)、化学物理学">物理化学(理论化学)、化学物理学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Gutman index&option=203" rel="nofollow">Gutman index;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Kirchhoff index&option=203" rel="nofollow">Kirchhoff index;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=multiplicative degree‐Kirchhoff index&option=203" rel="nofollow">multiplicative degree‐Kirchhoff index;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=spanning tree&option=203" rel="nofollow">spanning tree;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Wiener index&option=203" rel="nofollow">Wiener index;</a> </p> <div class="translation"> 机译:Gutman指数;Kirchhoff指数;乘法程度 - kirchhoff指数;生成树;维纳索引; </div> </li> </ul> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704019755894.html">Kirchhoff index, multiplicative degree‐Kirchhoff index and 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