using a triplestore implies that we will make use of a database which have a table with 3 coluns and 7 indexes? I am talking about utilizing a triple store always is relationed with this relational model?

From http://en.wikipedia.org/wiki/Triplestore:

A triplestore is really a purpose-built database for that storage and retrieval of Resource Description Framework (RDF) metadata.

It appears like this our prime-performance triplestores make use of a non-relational model:

Some triplestores happen to be built as database engines on your own, while some happen to be built on the top of existing commercial relational database engines (i.e. SQL-based).4 Such as the early growth and development of OLAP databases, this intermediate approach permitted large and effective database engines to become built for little programming effort within the first stages of triplestore development. Lengthy-term although it appears likely that native triplestores may have the benefit for performance. A problem with applying triplestores over SQL is the fact that although "triples" may thus be "saved", applying efficient querying of the graph-based RDF model (i.e. mapping from SPARQL) onto SQL queries is tough.5

Not always. You will find triplestores that depend on other RDBMS systems as backends. Good examples of the situation are: Jena/SDB, 3store or Virtuoso.

Others implement their very own native persistent model personalized to reply easier to the RDF data model, like 4store, Jena/TDB or BigData. These often scale better.

Conceptually, yes - a triple is really a binary relation having a subject, predicate, and object (e.g. <JohnSmith--marriedTo->JillSmith>.

Greater arity relations aren't possible inside a triple store because they are inside a normal RDBMS (if you can fake them via using multiple triples).

The implementation varies though, as previous solutions condition.

Most triple stores really store quads, to allow them to group triples into subsets ("Named Graphs" in RDF-speak).

The indexes are obviously optional, truly contained in some form - again frequently modified to support quads.