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Vector valued switching in signed graphs | ||
Communications in Combinatorics and Optimization | ||
مقاله 12، دوره 9، شماره 3، آذر 2024، صفحه 555-565 اصل مقاله (427.98 K) | ||
نوع مقاله: Original paper | ||
شناسه دیجیتال (DOI): 10.22049/cco.2023.28591.1624 | ||
نویسندگان | ||
Shahul K Hameed1؛ Albin Mathew2؛ K A Germina2؛ Thomas Zaslavsky* 3 | ||
1Department of Mathematics, K M M Government Women’s College, Kannur - 670004, Kerala, India | ||
2Department of Mathematics, Central University of Kerala, Kasaragod - 671316, Kerala, India | ||
3Department of Mathematics and Statistics, Binghamton University (SUNY), Binghamton, NY 13902-6000, USA | ||
چکیده | ||
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. | ||
کلیدواژهها | ||
Signed graph؛ vector valued switching؛ balancing dimension | ||
مراجع | ||
[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 | ||
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