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A construction for infinite families of semisymmetric graphs revealing their full automorphism group

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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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MLA
Cara, Philippe, Sara Rottey, and Geertrui Van de Voorde. “A Construction for Infinite Families of Semisymmetric Graphs Revealing Their Full Automorphism Group.” JOURNAL OF ALGEBRAIC COMBINATORICS 39.4 (2014): 967–988. Print.
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.
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): 967–988.
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.
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://dx.doi.org/10.1007/s10801-013-0475-4}},
  volume       = {{39}},
  year         = {{2014}},
}

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