Geodesic
About primitive regular graphs with exponent~2
Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 131-134

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Primitive regular graphs with exponent 2 are considered. We refine the known result that the number of edges of an undirected $n$-vertex graph with exponent 2 must be at least $(3n-3)/2$ for odd $n$ and $(3n-2)/2$ for an even $n$. For regular $n$-vertex graph with exponent 2 and $n>4$, the minimal number of edges is $2n$.
Keywords: primitive graph, exponent, regular graph.
Mots-clés : primitive matrix 
@article{PDMA_2017_10_a50,
     author = {M. B. Abrosimov and S. V. Kostin},
     title = {About primitive regular graphs with exponent~2},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {131--134},
     publisher = {mathdoc},
     number = {10},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2017_10_a50/}
}
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M. B. Abrosimov; S. V. Kostin. About primitive regular graphs with exponent~2. Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 131-134. http://geodesic.mathdoc.fr/item/PDMA_2017_10_a50/