%0 Journal Article
%T The Maximum and Minimum Value of Exponential Randić Indices of Quasi-Tree Graph
%A Lei Qiu
%A Xijie Ruan
%A Yan Zhu
%J Journal of Applied Mathematics and Physics
%P 1804-1818
%@ 2327-4379
%D 2024
%I Scientific Research Publishing
%R 10.4236/jamp.2024.125112
%X The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph <i>G</i> is defined as the sum of the weights <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <msup>
   <mi>e</mi>
   <mrow>
    <mstyle scriptlevel=' 1'>
     <mfrac>
      <mn>1</mn>
      <mrow>
       <msqrt>
        <mrow>
         <mi>d</mi><mrow><mo>(</mo>
          <mi>u</mi>
         <mo>)</mo></mrow><mi>d</mi><mrow><mo>(</mo>
          <mi>v</mi>
         <mo>)</mo></mrow></mrow>
       </msqrt>
       </mrow>
     </mfrac>
    </mstyle>
    </mrow>
  </msup>
  </mrow>
</math>
 of all edges <i>uv</i> of <i>G</i>, where <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>d</mi><mrow><mo>(</mo>
   <mi>u</mi>
  <mo>)</mo></mrow></mrow>
</math>
 denotes the degree of a vertex <i>u</i> in <i>G</i>. The paper mainly provides the upper and lower bounds of the exponential Randić index in quasi-tree graphs, and characterizes the extremal graphs when the bounds are achieved.
%K Exponential Randi&amp
%K #263
%K Index
%K Quasi-Tree Graph
%K Extremal Value
%K Extremal Graphs
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=133367