Complexity of this simple algorithm
<p>I did a algorithm to resolve a problem, but I don't know its complexity.
The algorithm verifies if all of the vertex of a graph are "good". A "good" vertex is a vertex that can access all  others vertexes of a graph following a path that started himself.</p>

<pre><code>public static boolean verify(Graph graph)
{
    for(int i=0; i &lt; graph.getVertex().size(); i++)
    {
        // List of vertexes visited 
        ArrayList&lt;Character&gt; accessibleVertex = new ArrayList&lt;Character&gt;();
        getChildren(graph.getVertex().get(i), graph.getVertex().get(i).getName(), accessibleVertex);    

        // If the count of vertex without father equals a count of the list of vertexes visited, his is a "good" vertex
        if((graph.getVertex().size()-1) == accessibleVertex.size())
            return true;
    }

    return false;
}

private static void getChildren(Vertex vertex, char fatherName, ArrayList&lt;Character&gt; accessibleVertex)
{
    // Ignore the 'father'
    if(vertex.getName() != fatherName)
        addIfUnique(vertex.getName(), accessibleVertex);

    for(int i=0; i &lt; vertex.getEdges().size(); i++)
    {
        getChildren(vertex.getEdges().get(i).otherVertex(), fatherName, accessibleVertex);
    }
}

private static void addIfUnique(char name, ArrayList&lt;Character&gt; accessibleVertex)
{
    boolean uniqueVertex = true;

    for(int i=0; i &lt; accessibleVertex.size(); i++)
    {
        if(accessibleVertex.get(i).equals(name))
            uniqueVertex = false;
    }

    if(uniqueVertex)
        accessibleVertex.add(name);
}
</code></pre>

<p><a href="http://i.stack.imgur.com/5MSXt.png" rel="nofollow">Graph tested</a></p>

<p>Thanks and sorry for my english.</p>