# Edge Product Number of Graphs in Paths

Keywords:
Edge function, edge product function, edge product graph, edge product number of graph and optimal edge product function

### Abstract

A graph G (V, E) is said to be a sum graph if there exists a bijective labeling from the vertex set V to a set S of positive integers such that (x y) ∈ E if and only if f(x) + f(y) ∈ S. In this paper, for a given graph G (V, E), the edge function, the edge product function and the edge product graph are introduced and studied. The edge product number of a graph is defined and the edge product numbers of paths is found.