Manila Journal of Science 10 (2017), pp. 126-130

On Modular Signatures of Some Autographs

Abstract

Let G = (V, E) be a graph where the edge set E can be a multiset. If there exists a bijection α: V → S(G) where S(G) is a multiset of real numbers such that uvE if and only if |α(u) − α(v)| = α(w) for some wV, then α is called an autograph labeling of G. The multiset S(G) = {α(v) : vV} is called a signature of G. If the underlying set of S(G) is {0,1,2,…,n − 1} where n = |V|, then S(G) is called a modular signature of G. Read More