Total graph of a signed graph

Francesco Belardo, Zoran Stanić, Tomas Zaslavsky

Abstract


The total graph is built by joining the graph to its line graph by means of the incidences. We introduce a similar construction for signed graphs. Under two similar defnitions of the line signed graph, we defne the corresponding total signed graph and we show that it is stable under switching. We consider balance, the frustration index and frustration number, and the largest
eigenvalue. In the regular case we compute the spectrum of the adjacency matrix of the total graph and the spectra of certain compositions, and we determine some with exactly two main eigenvalues.


Keywords


Bidirected graph, signed line graph, signed total graph, graph eigenvalues, regular signed graph, Cartesian product graph

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DOI: https://doi.org/10.26493/1855-3974.2842.6b5

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications