A function h is mentioned as a C -exponential mean labeling of a graph G V , E that has s vertices and r edges if h : V G ⟶ 1 , 2 , 3 , ⋯ , r + 1 is injective and the generated function h ∗ : E G ⟶ 2 , 3 , 4 , ⋯ , r + 1 defined by h ∗ a b = 1 / e h b h b / h a h a 1 / h b − h a , for all a b ∈ E G , is bijective. A graph which recognizes a C -exponential mean labeling is defined as   C -exponential mean graph. In the following study, we have studied the exponential meanness of the path, the graph triangular tree of T n , C m P n , cartesian product of two paths P m ▫ P n , one-sided step graph of S T n , double-sided step graph of 2 S T 2 n , one-sided arrow graph of A r s , double-sided arrow graph of D A r s , and subdivision of ladder graph S L t .