AUTHOR = {Germina, K.A. and Shahul Hameed, Koombail},
TITLE = {On composition of signed graphs},
JOURNAL = {Discuss. Math. Graph Theory},
FJOURNAL = {Discussiones Mathematicae Graph Theory},
VOLUME = {32},
YEAR = {2012},
NUMBER = {3},
PAGES = {507-516},
ISSN = {1234-3099},
ABSTRACT = {A graph whose edges are labeled either as positive or negative is called a
signed graph. In this article, we extend the notion of
composition of (unsigned) graphs (also called lexicographic
product) to signed graphs. We employ Kronecker product of
matrices to express the adjacency matrix of this product of
two signed graphs and hence find its eigenvalues when the
second graph under composition is net-regular. A signed graph
is said to be net-regular if every vertex has constant
net-degree, namely, the difference of the number of positive
and negative edges incident with a vertex. We also
characterize balance in signed graph composition and have
some results on the Laplacian matrices of this product.},