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Hameed, Shahul, Mathew, Albin, Germina, K A, Zaslavsky, Thomas. (1402). Vector valued switching in signed graphs. , (), -. doi: 10.22049/cco.2023.28591.1624
Shahul K Hameed; Albin Mathew; K A Germina; Thomas Zaslavsky. "Vector valued switching in signed graphs". , , , 1402, -. doi: 10.22049/cco.2023.28591.1624
Hameed, Shahul, Mathew, Albin, Germina, K A, Zaslavsky, Thomas. (1402). 'Vector valued switching in signed graphs', , (), pp. -. doi: 10.22049/cco.2023.28591.1624
Hameed, Shahul, Mathew, Albin, Germina, K A, Zaslavsky, Thomas. Vector valued switching in signed graphs. , 1402; (): -. doi: 10.22049/cco.2023.28591.1624

Vector valued switching in signed graphs

Communications in Combinatorics and Optimization
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 07 خرداد 1402    اصل مقاله (427.42 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, Associate Professor, K M M Government Women's College, Kannur, India.
2Department of Mathematics, Central University of Kerala, Kasaragod District, Kerala.
3Binghamton University, 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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