Vector valued switching in signed graphs

Document Type : Original paper

Authors

1 Department of Mathematics, K M M Government Women’s College, Kannur - 670004, Kerala, India

2 Department of Mathematics, Central University of Kerala, Kasaragod - 671316, Kerala, India

3 Department of Mathematics and Statistics, Binghamton University (SUNY), Binghamton, NY 13902-6000, USA

Abstract

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.

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References

[1] A. Dhamacharoen and P. Kasempin, The negative inner product sets, East-West J. Math. 12 (2010), no. 2, 207--216.
[2] T. Zaslavsky, Characterizations of signed graphs, J. Graph Theory 5 (1981), no. 4, 401--406.
https://doi.org/10.1002/jgt.3190050409
[3] Thomas Zaslavsky, Signed graphs, Discrete Appl. Math. 4 (1982), no. 1, 47--74.
https://doi.org/10.1016/0166-218X(82)90033-6
Communications in Combinatorics and Optimization
Volume 9, Issue 3
September 2024
Pages 555-565

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