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Applied Graph Theory
The maximum number of vertices of primitive regular graphs of orders $2, 3, 4$ with exponent $2$
M. B. Abrosimova, S. V. Kostinb, I. V. Losa a Saratov State University, Saratov, Russia
b MIREA — Russian Technological University, Moscow, Russia
Abstract:
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, primitive matrix, exponent, regular graph.
Citation:
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 $2$”, Prikl. Diskr. Mat., 2021, no. 52, 97–104
Linking options:
https://www.mathnet.ru/eng/pdm740 https://www.mathnet.ru/eng/pdm/y2021/i2/p97
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Abstract page: | 93 | Full-text PDF : | 33 | References: | 6 |
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