Geodesic
The maximum number of vertices of primitive regular graphs of orders $2, 3, 4$ with exponent~$2$
Prikladnaâ diskretnaâ matematika, no. 2 (2021), pp. 97-104

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In 2015, the results were obtained for the maximum number of vertices $ n_k $ in regular graphs of a given order $ k $ with a diameter $2$: $n_2 = 5$, $n_3 = 10$, $n_4 = 15$. In this paper, we investigate a similar question about the largest number of vertices $ np_k $ in a primitive regular graph of order $ k $ with exponent $2$. All primitive regular graphs with exponent $2$, except for the complete one, also have diameter $d =2 $. The following values were obtained for primitive regular graphs with exponent $2$: $np_2 = 3$, $np_3 = 4$, $np_4 = 11$.
Keywords: primitive graph, exponent, regular graph.
Mots-clés : primitive matrix 
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     author = {M. B. Abrosimov and S. V. Kostin and I. V. Los},
     title = {The maximum number of vertices of primitive regular graphs of orders $2, 3, 4$ with exponent~$2$},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {97--104},
     publisher = {mathdoc},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2021_2_a5/}
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M. B. Abrosimov; S. V. Kostin; I. V. Los. The maximum number of vertices of primitive regular graphs of orders $2, 3, 4$ with exponent~$2$. Prikladnaâ diskretnaâ matematika, no. 2 (2021), pp. 97-104. http://geodesic.mathdoc.fr/item/PDM_2021_2_a5/