Integral Cayley Graphs Generated by Distance Sets in Vector Spaces over Finite Fields (original) (raw)

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• Ngoc Dai Nguyen
• Minh Hai Nguyen
• Duy Hieu Do
• Anh Vinh Le

Keywords: integral graphs, cayley graphs, distance graphs

Abstract

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.

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How to Cite

Nguyen, N. D., Nguyen, M. H., Do, D. H., & Le, A. V. (2013). Integral Cayley Graphs Generated by Distance Sets in Vector Spaces over Finite Fields. The Electronic Journal of Combinatorics, 20(1), #P29. https://doi.org/10.37236/2730