The verb is used an a root in dependency structure.What if we have multiple verbs in a sentence, which one will be the root of sentence. also what will be the dependency relation between two verbs ???
The question of which verb is the root is largely settled among theoreticians, contrary to what lemontheme writes. The root is the finite verb, not the/a non-finite verb. This is the stance adopted by a large majority of established dependency grammars. Richard Hudson in his Word Grammar framework takes the finite verb as the root. Igor Mel'cuk in his Meanining-Text framework takes the finite verb as the root. The German schools (Eroms, Heringer, Gross, Engel, Lobin, etc.) take the finite verb as the root.
Lemontheme is correct only insofar as some computational linguists doing dependency grammar are unsure about the root. These computational linguists are, however, largely ignoring the large body of work that has accummulated over the decades in theoretical circles. Bliss in ignorance.
There are numerous empirical considerations that identify the finite verb as the root. The finite verb is the main locus of much functional information (person, number, tense, mood, voice). Subject-verb agreement obtains with the finite verb, not with the/a non-finite verb. In English, the finite verb is the left-most verb in the verb chain, making verb chains head-initial. In Japanese, the finite verb is the right-most verb in the verb chain, making verb chains head-final. There are thus broad typological considerations supporting the finite verb as the root.
Diagnostics for constituents of the sort that are widely employed in syntax, linguistics, and grammar textbooks support the finite verb as the root. This point will now be demonstrated here. Consider the following sentence:
(1) Fred has studied syntax.
If the finite verb has is the root here, then studied syntax is a complete subtree underneath has. If, in contrast, studied is the root, then studied syntax is not a complete subtree. Diagnostics for constituents settle the matter, since they clearly reveal that studied syntax is a complete subtree:
a. ...and studied syntax, Fred has. -- Topicalization b. Fred has done so. (done so = studied syntax) -- Proform substituion c. What Fred has done is studied syntax. -- Pseudoclefting d. What has Fred done? -- Studied syntax. -- Answer fragment e. Tom has studied syntax, and Fred has, too. -- VP-ellipsis
These examples illustrate that studied syntax is behaving as a coherent unit, i.e. as a complete subtree. This verifies that has is the root, since only if has is the root, does studied syntax qualify as a complete subtree. To state the point from another perspective, sentences (a-e) would all be bad if studied were the root over has.
The point about which verb is the root of the sentence is going to be delt with in detail at an upcoming Depling conference in Uppsala Sweden:
My coauthors and I will be presenting a number of papers, all of which demonstrate that, among other things, the finite verb is the root of the sentence. Whether the computational people (who want to take a non-finite verb as the root) will listen, though, remains to be seen. In any case, I will happily share these papers with anyone who wants more information. Contact me at firstname.lastname@example.org.
There are many types of dependency grammar and many types of dependency parsing. Some dependency parsers will generate as many isolated structures as possible and then try to find best way to combine them; in these cases, multiple verbs mean multiple roots to try out.
As for the best way to construe the dependency relation between verbs (such as one gets when one or more auxiliary verbs are present), this is still a topic of debate, so I'd rather not steer you in any particular direction.
Nevertheless, if it's the parsing side of things you're most interested in, I can recommend Kübler et al (2009) Dependency Parsing.
(Also, unless you're truly desperate for answers, one question mark generally suffices.)