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Connectivity and Diameter of Friends and Strangers Graphs Using Minimum Degree
Given graphs $X,Y$ on $n$ vertices, Defant and Kravitz defined the friends and strangers graph, denoted $\mathrm{FS}(X,Y)$. The vertices of $\mathrm{FS}(X,Y)$ are bijections $σ:V(X)\to V(Y)$, and two bijections $σ$ and $σ'$ are adjacent in $\mathrm{FS}(X,Y)$ if they differ by a transposition $(ab)$
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