A GRAPH OPERATION APPROACH TO LABELING WITH C-EXPONENTIAL MEANS

A function 𝜓 is referred to as a C-EML (in short C-EML) of a graph G(V, E) with q edges if 𝜓 : V (G) → {1, 2, 3, …, q + 1} is injective and the induced function 𝜓^* : E(G) → {2, 3, 4, …, q + 1} defined by $${\psi}^*(uv)={\Huge\lceil}{\frac{1}{e}}{\left({\frac{{\psi}(v)^{{\psi}(v)}}{{\psi}(u)^{{\psi}(u)}}}\right)^{\frac{1}{{\psi}(v)-{\psi}(u)}}}{\Huge\rceil},$$ for all uv ∈ E(G), is bijective. A graph that admits a C-EML is called a C-exponential mean graph (in short C-EMG). In this paper, we have discussed the exponential meanness of the path, the graph P_n(X₁, X₂, …, X_n), the twig graph TW(P_n), the graph P_n ⊙ S_m for m ≤ 3, the total graph of the path T(P_n), the graph P²_n, the middle graph of the path M(P_n), the graph P^b_a, the graph P_n ⊙ K₂, the graph arbitrary subdivision of S₃ and the graph P(1, 2, …, n - 1).