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A conjugate skew gain graph is a skew gain graph with the labels (alsocalled, the conjugate skew gains) from the field of complex numbes on theoriented edges such that they get conjugated when we reverse the orientation.In this paper we introduce distance matrices for conjugate skew gain graphs andcharacterize balanced conjugate skew gain graphs using these matrices. Weprovide explicit formulae for the distance spectra of certain conjugate skewgain graphs.

Distance Matrices for Conjugate Skew Gain Graphs