%0 Journal Article
%T 双圈图补图的距离无符号拉普拉斯谱半径<br>Distance Signless Laplacian Spectral Radius of the Complements of Bicyclic Graphs
%A 何若凡
%J Pure Mathematics
%P 293-301
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/pm.2025.151032
%X 设<i>G</i>是简单连通图&#65292;<math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <msup>
   <mi>D</mi>
   <mi>Q</mi>
  </msup>
  <mrow><mo>(</mo>
   <mi>G</mi>
  <mo>)</mo></mrow><mo>=</mo><mi>T</mi><mi>r</mi><mrow><mo>(</mo>
   <mi>G</mi>
  <mo>)</mo></mrow><mo>+</mo><mi>D</mi><mrow><mo>(</mo>
   <mi>G</mi>
  <mo>)</mo></mrow></mrow>
</math>

为图<i>G</i>的距离无符号拉普拉斯矩阵&#65292;其中<math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>T</mi><mi>r</mi><mrow><mo>(</mo>
   <mi>G</mi>
  <mo>)</mo></mrow></mrow>
</math>

和<math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>D</mi><mrow><mo>(</mo>
   <mi>G</mi>
  <mo>)</mo></mrow></mrow>
</math>

分别是图<i>G</i>的点传递对角矩阵和距离矩阵。本文在<i>n</i>阶双圈图补图中确定了距离无符号拉普拉斯谱半径最大时所落在的图类集合。<br>Let <i>G </i>be a simple connected graph, and <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <msup>
   <mi>D</mi>
   <mi>Q</mi>
  </msup>
  <mrow><mo>(</mo>
   <mi>G</mi>
  <mo>)</mo></mrow><mo>=</mo><mi>T</mi><mi>r</mi><mrow><mo>(</mo>
   <mi>G</mi>
  <mo>)</mo></mrow><mo>+</mo><mi>D</mi><mrow><mo>(</mo>
   <mi>G</mi>
  <mo>)</mo></mrow></mrow>
</math>

 be the distance signless Laplacian matrix of graph <i>G</i>, where <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>T</mi><mi>r</mi><mrow><mo>(</mo>
   <mi>G</mi>
  <mo>)</mo></mrow></mrow>
</math>

 and <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>D</mi><mrow><mo>(</mo>
   <mi>G</mi>
  <mo>)</mo></mrow></mrow>
</math>

 are diagonal matrix with vertex transmissions of <i>G </i>and distance matrix of <i>G</i>, respectively. This article determines the set of graph classes that fall at the maximum distance from signless Laplacian spectral radius in the complements of bicyclic graphs with <i>n</i>-order.
%K 距离无符号拉普拉斯矩阵&#65292
%K 谱半径&#65292
%K 双圈图&#65292
%K 补图<br>Distance Signless Laplacian Matrix
%K Spectral Radius
%K Bicyclic Graphs
%K Complements of Graphs
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=106679