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Hameed, Shahul, Mathew, Albin, Germina, K A, Zaslavsky, Thomas. (1403). Vector valued switching in signed graphs. , 9(3), 555-565. doi: 10.22049/cco.2023.28591.1624
Shahul K Hameed; Albin Mathew; K A Germina; Thomas Zaslavsky. "Vector valued switching in signed graphs". , 9, 3, 1403, 555-565. doi: 10.22049/cco.2023.28591.1624
Hameed, Shahul, Mathew, Albin, Germina, K A, Zaslavsky, Thomas. (1403). 'Vector valued switching in signed graphs', , 9(3), pp. 555-565. doi: 10.22049/cco.2023.28591.1624
Hameed, Shahul, Mathew, Albin, Germina, K A, Zaslavsky, Thomas. Vector valued switching in signed graphs. , 1403; 9(3): 555-565. doi: 10.22049/cco.2023.28591.1624

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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