A construction for infinite families of semisymmetric graphs revealing their full automorphism group
- Author
- Philippe Cara, Sara Rottey (UGent) and Geertrui Van de Voorde (UGent)
- Organization
- Abstract
- We give a general construction leading to different non-isomorphic families of connected q-regular semisymmetric graphs of order 2q (n+1) embedded in , for a prime power q=p (h) , using the linear representation of a particular point set of size q contained in a hyperplane of . We show that, when is a normal rational curve with one point removed, the graphs are isomorphic to the graphs constructed for q=p (h) in Lazebnik and Viglione (J. Graph Theory 41, 249-258, 2002) and to the graphs constructed for q prime in Du et al. (Eur. J. Comb. 24, 897-902, 2003). These graphs were known to be semisymmetric but their full automorphism group was up to now unknown. For qa parts per thousand yenn+3 or q=p=n+2, na parts per thousand yen2, we obtain their full automorphism group from our construction by showing that, for an arc , every automorphism of is induced by a collineation of the ambient space . We also give some other examples of semisymmetric graphs for which not every automorphism is induced by a collineation of their ambient space.
- Keywords
- Linear representation, Automorphism group, Semisymmetric graph, Arc, Normal rational curve, 3 FUNDAMENTAL PROBLEMS, Q EVEN, LINEAR REPRESENTATIONS, MDS-CODES, B-SEGRE, K-ARCS, PG(N_Q)
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-5807925
- MLA
- Cara, Philippe, et al. “A Construction for Infinite Families of Semisymmetric Graphs Revealing Their Full Automorphism Group.” JOURNAL OF ALGEBRAIC COMBINATORICS, vol. 39, no. 4, 2014, pp. 967–88, doi:10.1007/s10801-013-0475-4.
- APA
- Cara, P., Rottey, S., & Van de Voorde, G. (2014). A construction for infinite families of semisymmetric graphs revealing their full automorphism group. JOURNAL OF ALGEBRAIC COMBINATORICS, 39(4), 967–988. https://doi.org/10.1007/s10801-013-0475-4
- Chicago author-date
- Cara, Philippe, Sara Rottey, and Geertrui Van de Voorde. 2014. “A Construction for Infinite Families of Semisymmetric Graphs Revealing Their Full Automorphism Group.” JOURNAL OF ALGEBRAIC COMBINATORICS 39 (4): 967–88. https://doi.org/10.1007/s10801-013-0475-4.
- Chicago author-date (all authors)
- Cara, Philippe, Sara Rottey, and Geertrui Van de Voorde. 2014. “A Construction for Infinite Families of Semisymmetric Graphs Revealing Their Full Automorphism Group.” JOURNAL OF ALGEBRAIC COMBINATORICS 39 (4): 967–988. doi:10.1007/s10801-013-0475-4.
- Vancouver
- 1.Cara P, Rottey S, Van de Voorde G. A construction for infinite families of semisymmetric graphs revealing their full automorphism group. JOURNAL OF ALGEBRAIC COMBINATORICS. 2014;39(4):967–88.
- IEEE
- [1]P. Cara, S. Rottey, and G. Van de Voorde, “A construction for infinite families of semisymmetric graphs revealing their full automorphism group,” JOURNAL OF ALGEBRAIC COMBINATORICS, vol. 39, no. 4, pp. 967–988, 2014.
@article{5807925, abstract = {{We give a general construction leading to different non-isomorphic families of connected q-regular semisymmetric graphs of order 2q (n+1) embedded in , for a prime power q=p (h) , using the linear representation of a particular point set of size q contained in a hyperplane of . We show that, when is a normal rational curve with one point removed, the graphs are isomorphic to the graphs constructed for q=p (h) in Lazebnik and Viglione (J. Graph Theory 41, 249-258, 2002) and to the graphs constructed for q prime in Du et al. (Eur. J. Comb. 24, 897-902, 2003). These graphs were known to be semisymmetric but their full automorphism group was up to now unknown. For qa parts per thousand yenn+3 or q=p=n+2, na parts per thousand yen2, we obtain their full automorphism group from our construction by showing that, for an arc , every automorphism of is induced by a collineation of the ambient space . We also give some other examples of semisymmetric graphs for which not every automorphism is induced by a collineation of their ambient space.}}, author = {{Cara, Philippe and Rottey, Sara and Van de Voorde, Geertrui}}, issn = {{0925-9899}}, journal = {{JOURNAL OF ALGEBRAIC COMBINATORICS}}, keywords = {{Linear representation,Automorphism group,Semisymmetric graph,Arc,Normal rational curve,3 FUNDAMENTAL PROBLEMS,Q EVEN,LINEAR REPRESENTATIONS,MDS-CODES,B-SEGRE,K-ARCS,PG(N_Q)}}, language = {{eng}}, number = {{4}}, pages = {{967--988}}, title = {{A construction for infinite families of semisymmetric graphs revealing their full automorphism group}}, url = {{http://doi.org/10.1007/s10801-013-0475-4}}, volume = {{39}}, year = {{2014}}, }
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