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Mathematics > Combinatorics

arXiv:2208.00149 (math)
[Submitted on 30 Jul 2022 (v1), last revised 19 May 2023 (this version, v3)]

Title:Vector Valued Switching in Signed Graphs

Authors:Shahul Hameed K, Albin Mathew, Germina K A, Thomas Zaslavsky
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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.
Comments: 15 pp., 5 figs. V2 12 pp., 4 figs., more data, slightly shorter. V3 typos fixed
Subjects: Combinatorics (math.CO)
MSC classes: 05C22
Cite as: arXiv:2208.00149 [math.CO]
  (or arXiv:2208.00149v3 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.2208.00149

Submission history

From: Thomas Zaslavsky [view email]
[v1] Sat, 30 Jul 2022 05:57:45 UTC (11 KB)
[v2] Thu, 20 Apr 2023 03:14:02 UTC (10 KB)
[v3] Fri, 19 May 2023 21:29:19 UTC (10 KB)
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