If the vertices of a graph Γ(α, β), with α = |V(Γ)| and β = |E(Γ)|, can be labelled with unequal integers within the set [0, 2β – 1], so that the edges labels generated by the sum of the labels of the end vertices modulo 2β are distinct odd numbers from the set [1, 2β – 1]. Then, we regard the graph Γ(V, E) to be a semi-odd harmonic graph. An odd harmonious graph satisfies the additional condition that modular asthmatic is not done. A strong odd harmonious graph is defined as an odd harmonious graph whose vertices can be labelled with unequal integers from the set [0, β]. In this study, we introduce semi-odd harmonious labeling, which is an extension of odd harmonious labeling. We establish the existence of semi-odd harmonious labeling for the super subdivision of the following graphs: Y–tree, the graph Tg, g–2, the graph Pg ○K1, as well as the twig and crown graph. We demonstrate odd harmonious labeling for the super subdivision of the subsequent graphs: cycle, dragon graph Pm(Cg), wheel graph, friendship graph Frg, dumbbell graph Dbm,g, fan graph and the helm graph. The presence of strong odd harmonious labeling for the super subdivision is shown in the final section.