Vector valued switching in the products of signed graphs

Document Type : Original paper


1 Department of Mathematics, Central University of Kerala, Kasaragod District, Kerala.

2 Central University of Kerala, Kasaragod, India


A signed graph is a graph whose edges are labeled either as positive or negative. The concepts of vector valued switching and balancing dimension of signed graphs were introduced by S. Hameed et al. In this paper, we deal with the balancing dimension of various products of signed graphs, namely the Cartesian product, the lexicographic product, the tensor product, and the strong product.


Main Subjects

[1] M. Brunetti, M. Cavaleri, and A. Donno, Erratum to the article’a lexicographic product for signed graphs’., Australas. J. Combin. 75 (2019), 256–258.
[2] M. Brunetti, M. Cavaleri, and A. Donno, A lexicographic product for signed graphs., Australas. J. Combin. 74
(2019), 332–343.
[3] K.A. Germina, T. Zaslavsky, and S.K. Hameed, On products and line graphs of signed graphs, their eigenvalues and energy, Linear Algebra Appl. 435 (2011), no. 10, 2432–2450.
[4] S.K. Hameed and K.A. Germina, On composition of signed graphs, Discuss. Math. Graph Theory 32 (2012), no. 3, 507–516.
[5] S.K. Hameed, A. Mathew, K.A. Germina, and T. Zaslavsky, Vector valued switching in signed graphs, Commun. Comb. Optim., (In press)
[6] F. Harary, Graph Theory, Addison Wesley, Reading, Mass., 1969.
[7] D. Lajou, On Cartesian products of signed graphs, Discrete Appl. Math. 319 (2022), 533–555.
[8] V. Mishra, Graphs associated with (0, 1) and (0, 1, −1) matrices, Phd thesis, IIT Bombay, 1974.
[9] D. Sinha and P. Garg, Balance and antibalance of the tensor product of two signed graphs, Thai J. Math. 12 (2013), no. 2, 303–311.
[10] T. Zaslavsky, Signed graphs, Discrete Appl. Math. 4 (1982), no. 1, 47–74.
[11] T. Zaslavsky, A mathematical bibliography of signed and gain graphs and allied areas, Electron. J. Comb. (2018), Article ID: DS8.