For any directed graph $G,$ let $f(G)($resp$.,g(G))$ denote the minimum

$($resp$.,$ maximum$)$ number of edges labeled as back edges in any DFS traversal of $G.$

$($a$)($poimts$)$ Use a result presented in class to explain why the following claim holds: For all

directed graphs $G$ such that $g(G)>0,$ we have $f(G)>0.$

$($b$)$

Prove or disprove: For all directed graphs $G,$ we have $f(G)=g(G).$