Balance theory: An extension to conjugate skew gain graphs

Document Type : Original paper

Authors

Department of Mathematics, K M M Government Women’s College, Kannur - 670004, Kerala, India

Abstract

We extend the notion of balance from the realm of signed and gain graphs to conjugate skew gain graphs which are skew gain graphs where the labels on the oriented edges get conjugated when we reverse the orientation. We characterize the balance in a conjugate skew gain graph in several ways especially by dealing with its adjacency matrix and the $g$-Laplacian matrix. We also deal with the concept of anti-balance in conjugate skew gain graphs.

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References

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Communications in Combinatorics and Optimization
Volume 9, Issue 2
June 2024
Pages 253-262

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