DG argues that two words in a sentence have a dependent relation if one word depends on the second one. Look at the following examples:

a. Mary's friend 'Mary' depends on 'friend'.
b. arrived late 'late' depends on 'arrived'.
c. summer night 'summer' depends on 'night'.
d. in the evening 'in' the evening' depends on 'in'.
e. terribly sorry 'terribly' depends on 'sorry'.

Now, let's turn our attention to the way DG theorists look at verbs. Much different from the viewpoint of traditional grammar you've studied, and fairly different from other approaches in syntax study, They divide verbs into:

1. Intransitive verbs: The very basic definition of an intransitive verb is 'the verb that takes only one dependent'. This first definition introduced is sufficient to classify verbs in the following sentences into 'intransitive verbs'.
f. Joshua smiled.
g. Jen went to bed late.
h. The telephone is ringing.
i. The Smiths appeared happy.

Interestingly enough, however, some intransitive verbs take two dependents.
j. Jen resembled her mother.
k. Joshua always has smiles on his face.

Would you argue that according to your traditional grammar notion, 'have' is a transitive verb? Let's see what DG linguists have to prove that it is not.
Traditional grammar define a 'transitive verb' as the verb that is followed by an object. You've also studied 'passive voice' where the object of a transitive verb is moved to the subject position as in
Now go back to sentence j. and k. Try passivizing the two sentences:
l. *Her mother is resembled by Jen.
m. *Smiles are always had by Joshua on his face.

You may start to be convinced by the way DG looks at these data. Now let's back up to our intransitive verbs with one dependent. Still there are two sub-set of intransitive verbs in that group. Consider the following set of sentences:
n. Seven dwarfs lived in the wood.
o. The new manager came.
p. The temperature dropped.
Verbs of movement or change-of-state verbs as in n. and o. can appear in 'there' sentences, but the ergative verb as in p. cannot.
q. There lived in the wood seven dwarfs .
r . There came the new manager.
s. *There dropped the temperature.