%0 Journal Article
%T Note on &#8220;Sharp Isolated Toughness Bound for Fractional <math xmlns='http://www.w3.org/1998/Math/MathML'> <mrow>  <mrow><mo>(</mo>   <mrow>    <mi>k</mi><mo>,</mo><mi>m</mi></mrow>  <mo>)</mo></mrow></mrow></math>-Deleted Graphs&#8221;
%A Wei Gao
%J Journal of Applied Mathematics and Physics
%P 365-380
%@ 2327-4379
%D 2025
%I Scientific Research Publishing
%R 10.4236/jamp.2025.132017
%X As an appendix of [Gao <i>et al</i>. Sharp isolated toughness bound for fractional <math xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mrow><mo>(</mo>
   <mrow>
    <mi>k</mi><mo>,</mo><mi>m</mi></mrow>
  <mo>)</mo></mrow></mrow>
</math>

-deleted graphs, Acta Mathematicae Applicatae Sinica, English Series, 2025, 41(1): 252-269], the detailed proof of Theorem 4.1 in this work is presented.
%K Graph
%K Isolated Toughness Variant
%K Fractional -Deleted Graph
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=140467