Vector valued switching in signed graphs

Document Type : Original paper


1 Department of Mathematics, Associate Professor, K M M Government Women's College, Kannur, India.

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

3 Binghamton University, Binghamton, NY 13902-6000, USA


A signed graph is a graph with edges marked positive and negative; it is unbalanced if some cycle has negative sign product. We introduce the concept of vector valued switching function in signed graphs, which extends the concept of switching to higher dimensions. Using this concept, we define balancing dimension and strong balancing dimension for a signed graph, which can be used for a new classification of degree of imbalance of unbalanced signed graphs. We provide bounds for the balancing and strong balancing dimensions, and calculate these dimensions for some classes of signed graphs.


Main Subjects

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