Journal of the Iranian Mathematical Society

Journal of the Iranian Mathematical Society

Analysis of balance in the products of conjugate Skew Gain graphs

Document Type : Research Article

Authors
K. Biju 1
K. Shahul Hameed 2
1 Department of Mathematics, PRNSS College, Mattanur, Kannur University, Kerala, India.
2 Research Supervisor Hermann Gundert Central Library, Kannur University, Kerala, India
10.30504/jims.2026.547899.1285
Abstract
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.
Keywords
Conjugate skew gain graph&lrm
balance&lrm
Cartesian product&lrm
Lexicographic product&lrm
, Tensor product
Subjects
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Journal of the Iranian Mathematical Society
Volume 7, Issue 1
This issue is in progress but all papers are fully citable
February 2026
Pages 13-23