Distance Matrices for Conjugate Skew Gain Graphs
Shahul Hameed K, Ramakrishnan K O, Biju K
TL;DR
This paper introduces distance matrices for conjugate skew gain graphs, characterizes their balanced forms, and provides explicit formulas for their distance spectra, advancing spectral graph theory in complex gain graphs.
Contribution
It defines distance matrices for conjugate skew gain graphs and characterizes balanced graphs using these matrices, including explicit spectral formulas.
Findings
Distance matrices for conjugate skew gain graphs are introduced.
Balanced conjugate skew gain graphs are characterized via these matrices.
Explicit formulas for the distance spectra of certain graphs are provided.
Abstract
A conjugate skew gain graph is a skew gain graph with the labels (also called, the conjugate skew gains) from the field of complex numbes on the oriented edges such that they get conjugated when we reverse the orientation. In this paper we introduce distance matrices for conjugate skew gain graphs and characterize balanced conjugate skew gain graphs using these matrices. We provide explicit formulae for the distance spectra of certain conjugate skew gain graphs.
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Taxonomy
Topicsgraph theory and CDMA systems · Graph theory and applications · Matrix Theory and Algorithms