Sum signed graphs - I

Let G=(V,E) be a simple graph, f : V(G) → {1, 2, …, |V(G)|} be a bijective function and σ : E(G) → {+,-} be a mapping such that σ (uv)=+, whenever f(u)+f(v) ≤ n and σ (uv)=-, whenever f(u)+f(v)>n. Then, S=(G,f,σ ) is said to be a sum signed graph. In this paper, we initiate the study of sum signed graphs. Also, we find rna number for some classes of graphs and present some of the characteristics of sum signed graphs.