Vector Valued Switching in Signed Graphs
Combinatorics
2023-05-23 v3
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.
Keywords
Cite
@article{arxiv.2208.00149,
title = {Vector Valued Switching in Signed Graphs},
author = {Shahul Hameed K and Albin Mathew and Germina K A and Thomas Zaslavsky},
journal= {arXiv preprint arXiv:2208.00149},
year = {2023}
}
Comments
15 pp., 5 figs. V2 12 pp., 4 figs., more data, slightly shorter. V3 typos fixed