학술논문
Total graph of a signed graph.
Document Type
Journal
Author
Belardo, Francesco (I-NAPL-AM) AMS Author Profile; Stanić, Zoran (SE-BELGM) AMS Author Profile; Zaslavsky, Thomas (1-SUNY2) AMS Author Profile
Source
Subject
05 Combinatorics -- 05C Graph theory
05C50Graphs and linear algebra
05C76Graph operations
05C50
05C76
Language
English
Abstract
Summary: ``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.''