ABSTRACT. 

Let η ≥ 3 be an integer with primitive root π. For a simple connected graph G of order n, a bijective function f : V (G) → {1, 2, …, n} is called a logarithmic cordial labeling to the base π modulo η if the induced function f ∗ π,η : E(G) → {0, 1}, defined by f ∗ π,η(ab) = 0 if indπ,η(f(a) + f(b)) ≡ 0(mod 2) or gcd(f(a) + f(b), η) ̸= 1, and f ∗ π,η(ab) = 1 if indπ,η(f(a) + f(b)) ≡ 1(mod 2), satisfies the condition |ef∗π,η (0) − ef∗π,η (1)| ≤ 1 where ef∗π,η (i) is the number of edges with label i(i = 0, 1). In this paper, we study the logarithmic cordial labeling of various classes of graphs, including path graphs, cycle graphs, star graphs, and complete graphs.