On the translation of an autograph - Fontanil, Lauro L. (Philippine computing journal)
A graph G is an autograph if its vertices can be labeled bi-jectively by a multiset S of numbers called signature such that two vertices are adjacent if and only if the absolute difference of the corresponding labels is also in S. Given a signature S and its corresponding autograph G(S), the autograph with signature whose elements resulted from adding a fixed real number to every element of S is called a translation of G(S). In this study, properties of translations of autographs were determined. These include the number of edges a translation consists and some necessary conditions for two translations to be isomorphic. The exact number of nonempty translations of an autograph with signature consisting of integers was also found. This result is a refinement of the previous one which only gives bounds on the number of nonempty translations an autograph could have.