Check if a graph is a tree

Python Help
1

I’m learning graphs and can’t solve this task. As I understand there are 2 conditions for graph being a tree:

  1. vertices must be connected

  2. there is no cycle

To check for connectivity I am using dfs

graph = []
visited = []

def dfs(v):
    visited[v] = True
    for u in graph[v]:
        if not visited[u]:
            dfs(u)

the main function is

def isTree(adj_list):
    global graph, visited
    n = len(adj_list)

    graph = adj_list
    visited = [False for i in range(n)]

    is_tree = True

    # MY CODE STARTS HERE
    for v in range(n):
        if not visited[v]:
            dfs(v)
        elif v in graph[-1]:
            is_tree = False
     # END OF CODE
    return is_tree

adj_list = [[1,2], [0], [0]]
print(isTree(adj_list))

I thought condition elif would check for cycling. But it doesn’t look so.