Consider the degree histogram below. Note that $H(k^{*})$ should be treated as a variable and the symbol : denotes that the values in the vertical axis less or equal than $14$ are located exactly on visible markings of the plot. Any value above $14$ on the vertical axis shows incomplete information, and thus, the markings on the plot should not be taken literally.

$($a$)[1$ point$]$ Calculate $n,m,,$ and $($:$k$:$).$ HINT: Your results should be a function of $H(k^{*})$

$($b$)[1$ point$]$ What is the minimum value of $H(k^{*})?$

$($c$)[1$ point$]$ Using your result from part b$,$ Calculate $n,m,,$ and $<k>$