%0 Journal Article %T Note on “Sharp Isolated Toughness Bound for Fractional ( k,m )-Deleted Graphs” %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 et al. Sharp isolated toughness bound for fractional ( k,m ) -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