Oriented gain graphs, line graphs and eigenvalues

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Oriented gain graphs, line graphs and eigenvalues

Reff, Nathan

Linear algebra and its applications, 10/2016, Volume: 506

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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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Reff, Nathan

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