Geodesic
Integral Cayley graphs generated by distance sets in vector spaces over finite fields
Ngoc Dai Nguyen1 ; Minh Hai Nguyen2 ; Duy Hieu Do2 ; Anh Vinh Le3
1School of Applied Mathematics and Informatics, Hanoi University of Science and Technology
2Faculty of Mathematics, Mechanics and Informatics, Hanoi University of Science, VNU-Hanoi
3Vietnam National University, Hanoi
The electronic journal of combinatorics, Tome 20 (2013) no. 1
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Si Li and the fourth listed author (2008) considered unitary graphs attached to the vector spaces over finite rings using an analogue of the Euclidean distance. These graphs are shown to be integral when the cardinality of the ring is odd or the dimension is even. In this paper, we show that the statement also holds for the remaining case: the cardinality of the ring is even and the dimension is odd, by showing a sufficient condition for Cayley graphs generated by distance sets in vector spaces over finite fields to be integral.
DOI : 10.37236/2730
Classification : 05C25, 05C12
Mots-clés : integral graphs, Cayley graphs, distance graphs

Ngoc Dai Nguyen  1   ; Minh Hai Nguyen  2   ; Duy Hieu Do  2   ; Anh Vinh Le  3

1 School of Applied Mathematics and Informatics, Hanoi University of Science and Technology
2 Faculty of Mathematics, Mechanics and Informatics, Hanoi University of Science, VNU-Hanoi
3 Vietnam National University, Hanoi 
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     author = {Ngoc Dai Nguyen and Minh Hai Nguyen and Duy Hieu Do and Anh Vinh Le},
     title = {Integral {Cayley} graphs generated by distance sets in vector spaces over finite fields},
     journal = {The electronic journal of combinatorics},
     year = {2013},
     volume = {20},
     number = {1},
     doi = {10.37236/2730},
     zbl = {1266.05060},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2730/}
}
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Ngoc Dai Nguyen; Minh Hai Nguyen; Duy Hieu Do; Anh Vinh Le. Integral Cayley graphs generated by distance sets in vector spaces over finite fields. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2730

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