Best Way To Represent Graph for the Petersen Graph problem

I am having a hard time representing graphs. Mostly the books that I have referred shows a description using classes. I want to use the STL and not classes.
http://www.codechef.com/problems/PETERSEN -

Also, any tutorial that discusses representation of trees in C++ ?

Read from—

  1. Coreman.
  2. competitive programming book by steven and felix halim.

just google search them and download the pdf