Shortest Path Algorithm

[Ehump20]

public void unweighted( String startName )
    {
        clearAll( );

        Vertex start = vertexMap.get( startName );
        if( start == null )
            throw new NoSuchElementException( "Start vertex not found" );

        Queue<Vertex> q = new LinkedList<Vertex>( );
        q.add( start ); start.dist = 0;

        while( !q.isEmpty( ) )
        {
            Vertex v = q.remove( );

            for( Edge e : v.adj )
            {
                Vertex w = e.dest;
                if( w.dist == INFINITY )
                {
                    w.dist = v.dist + 1;
                    w.prev = v;
                    q.add( w );
                }
            }
        }
    }

For the unweighted shortest path algorithm, how would you change this code so that it searches for the minimum-cost vertex as a sequential scan of the vertex table? Thanks.