On the Laplacian Eigenvalues of Signed Graphs

Please enable javascript in your browser.

Dodongeh, Ebrahim | 2017

1012 Viewed

Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 50365 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Akbari, Saieed
Abstract:
A signed graph is a graph with a sign attached to each edge. This article extends some fundamental concepts of the Laplacian matrices from graphs to signed graphs.In particular, the largest Laplacian eigenvalue of a signed graph is investigated,which generalizes the corresponding results on the largest Laplacian eigenvalue of a graph.It is proved that (C2n+1; +) is uniquely determined by its Laplacian spectrum (or is DLS), where (C2n+1; +) is a signed cycle in which all edges have positive sign. On the other hand, we determine all Laplacian cospectral mates of (C2n; +) and hence (C2n; +) is not DLS. Also, we show that for every positive integer n, (Cn;) is DLS. Then, we study the spectrum of the adjacency matrix of signed cycles. It is shown that both signed cycles (C2n+1; +) and (C2n+1; ) are uniquely determined by their spectrum (or they are DS). Moreover, (C2n;) and (C2n; +) are not DS
Keywords:
Laplacian Eigen Values ; Balance ; Signed Graph ; Switching Equivalent