Iranian Mathematical Society Journal of the Iranian Mathematical Society 2717-1612 7 1 2026 02 01 Analysis of balance in the products of conjugate Skew Gain graphs 13 23 239013 10.30504/jims.2026.547899.1285 EN K. Biju Department of Mathematics, PRNSS College, Mattanur, Kannur University, Kerala, India. 0000-0002-8809-8019 K. Shahul Hameed Research Supervisor Hermann Gundert Central Library, Kannur University, Kerala, India 0000-0003-0905-3865 Journal Article 2025 09 18 A conjugate skew gain graph is a graph whose edges are oriented and assigned labels—termed edge skew gains—from the multiplicative group $\mathbb{C}^\times$ of nonzero complex numbers‎, ‎such that reversing the orientation of an edge replaces its label with its complex conjugate‎. ‎In this article‎, ‎we define various products of conjugate skew gain graphs such as the cartesian product‎, ‎the lexicographic product‎, ‎the strong product, and the tensor product‎. ‎We characterize the balance in these product graphs in terms of the balance of the constituent conjugate skew gain graphs‎. https://jims.ims.ir/article_239013_fa9b6fd7c8a6f8e4f16a40fd1b58b4aa.pdf