Total graph of a signed graph
Combinatorics
2021-06-21 v3
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 definitions of the line signed graph, we define 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
Cite
@article{arxiv.1908.02001,
title = {Total graph of a signed graph},
author = {Francesco Belardo and Zoran Stanić and Thomas Zaslavsky},
journal= {arXiv preprint arXiv:1908.02001},
year = {2021}
}
Comments
This versions has been largely revised by the three authors and submitted to journals. The manuscript consists of 15 pages and 2 figures