ABSTRACT
A signed graph is a pair , where
is a graph and
is the sign function on the edges of G. For a signed graph we consider the Laplacian matrix defined as
, where
is the matrix of vertex degrees of G and the (signed) adjacency matrix
. A signed ∞-graph consists of two signed cycles with just one vertex in common. In this paper, we study the Laplacian spectral determination problem for the class of signed ∞-graphs, and we identify all connected L-cospectral mates.
Acknowledgments
The authors are grateful to the unknown referee for the useful remarks which has led to an improvement of the results presentation.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCID
Francesco Belardo http://orcid.org/0000-0003-4253-2905
Maurizio Brunetti http://orcid.org/0000-0002-2742-1919