Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21289320240901Vector valued switching in signed graphs5555651457010.22049/cco.2023.28591.1624ENShahul KHameedDepartment of Mathematics, K M M Government Womenâ€™s College, Kannur - 670004, Kerala, IndiaAlbinMathewDepartment of Mathematics, Central University of Kerala, Kasaragod - 671316, Kerala, India0000-0002-2643-3416K AGerminaDepartment of Mathematics, Central University of Kerala, Kasaragod - 671316, Kerala, India0000-0002-2643-3416ThomasZaslavskyDepartment of Mathematics and Statistics, Binghamton University (SUNY), Binghamton, NY
13902-6000, USAJournal Article20230420A 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.http://comb-opt.azaruniv.ac.ir/article_14570_a32562d8b382a20dbf15525d6d96d990.pdf