@article{, 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 = {507516}, ISSN = {12343099}, 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 netregular. A signed graph is said to be netregular if every vertex has constant netdegree, 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.}, }
