اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدRemarks on the spectral radius of $K_{r+1}$-saturated graphs
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تأليف
V. Nikiforov
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Write $rholeft( Gright) $ for the spectral radius of a graph $G$ and $S_{n,r}$ for the join $K_{r}veeoverline{K}_{n-r}.$ Let $n>rgeq2$ and $G$ be a $K_{r+1}$-saturated graph of order $n.$ Recently Kim, Kim, Kostochka, and O determined exactly the minimum value of $rholeft( Gright) $ for $r=2$, and found an asymptotically tight bound on $rholeft( Gright) $ for $rgeq3.$ They also conjectured that [ rholeft( Gright) >rholeft( S_{n,r-1}right) , ] unless $G=S_{n,r-1}.$ In this note their conjecture is proved.
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