Oriented Gain Graphs, Line Graphs and Eigenvalues
Combinatorics
2015-06-17 v1
Abstract
A theory of orientation on gain graphs (voltage graphs) is developed to generalize the notion of orientation on graphs and signed graphs. Using this orientation scheme, the line graph of a gain graph is studied. For a particular family of gain graphs with complex units, matrix properties are established. As with graphs and signed graphs, there is a relationship between the incidence matrix of a complex unit gain graph and the adjacency matrix of the line graph.
Keywords
Cite
@article{arxiv.1506.05059,
title = {Oriented Gain Graphs, Line Graphs and Eigenvalues},
author = {Nathan Reff},
journal= {arXiv preprint arXiv:1506.05059},
year = {2015}
}