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arXiv · 1506.05059

Oriented Gain Graphs, Line Graphs and Eigenvalues

Nathan Reff
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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.

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Nathan Reff. 2015-06-16. Oriented Gain Graphs, Line Graphs and Eigenvalues. https://arxiv.org/abs/1506.05059

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