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A construction of small regular bipartite graphs of girth 8

Abstract : Let q be a prime a power and k an integer such that 3 ≤ k ≤ q. In this paper we present a method using Latin squares to construct adjacency matrices of k-regular bipartite graphs of girth 8 on 2(kq2 -- q) vertices. Some of these graphs have the smallest number of vertices among the known regular graphs with girth 8.
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Camino Balbuena. A construction of small regular bipartite graphs of girth 8. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2009, Vol. 11 no. 2 (2), pp.33--46. ⟨10.46298/dmtcs.461⟩. ⟨hal-00988211⟩

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