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 
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     title = {About primitive regular graphs with exponent~2},
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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/

[1] Wielandt H., “Unzerlegbare nicht negative Matrizen”, Math. Zeitschr., 52 (1950), 642–648 | DOI | MR | Zbl

[2] Jin M., Lee S. G., Seol H. G., “Exponents of $r$-regular primitive matrices”, Inform. Center Math. Sciences, 6:2 (2003), 51–57

[3] Bueno M. I., Furtado S., “On the exponent of $r$-regular primitive matrices”, ELA. Electronic J. Linear Algebra, 17 (2008), 28–47 | MR | Zbl

[4] Kim B., Song B., Hwang W., “Nonnegative primitive matrices with exponent 2”, Linear Algebra and its Applications, 407 (2005), 162–168 | DOI | MR | Zbl

[5] Meringer M., “Fast generation of regular graphs and construction of cages”, J. Graph Theory, 30 (1999), 137–146 | 3.0.CO;2-G class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[6] Sukhov S. A., DSR Generator, Svid. o gos. registratsii programmy dlya EVM No 2016610073. Zaregistrirovano v Reestre programm dlya EVM 11 yanvarya 2016 g.

[7] Kostin S. V., “Ob ispolzovanii zadach po teorii grafov dlya intellektualnogo razvitiya uchaschikhsya”, Matematika v obrazovanii: sb. statei, 10, ed. I. S. Emelyanova, Izd-vo Chuvash. un-ta, Cheboksary, 2014, 68–74