$(15$ pts$)$ In the graph shown below, determine whether the following walks are trails, paths, closed walks, circuits, simple circuits, or just walks.

$($a$)v_0{e}_1{v}_1{e}_{10}{v}_5{e}_9{v}_2{e}_2{v}_1$

$($b$)v_4{e}_7{v}_2{e}_9{v}_5{e}_{10}{v}_1{e}_3{v}_2{e}_9{v}_5$

$($c$)v_2$

$($d$)v_5{v}_2{v}_3{v}_4{v}_4{v}_5$

$($e$)v_2{v}_3{v}_4{v}_5{v}_2{v}_4{v}_3{v}_2$

$($f$)e_5{e}_8{e}_{10}{e}_3$How to solve