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Эта публикация цитируется в 5 научных статьях (всего в 5 статьях)
Дискретная математика и математическая кибернетика
Строение вектора разнообразия шаров типичного графа заданного диаметра
Т. И. Федоряева Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
Аннотация:
For labeled $n$-vertex graphs with fixed diameter $d\geq 1$, the diversity vectors of balls (the ith component of the vector is equal to the number of different balls of radius $i$) are studied asymptotically. An explicit description of the diversity vector of balls of a typical graph with given diameter is obtained. A set of integer vectors $\Lambda_{n,d}$ consisting of $\lfloor\frac{d-1}{2}\rfloor$ different vectors for $d\geq 5$ and a unique vector for $d<5$ is found. It is proved that almost all labeled $n$-vertex graphs of diameter $d$ have the diversity vector of balls belonging to $\Lambda_ {n,d}$. It is established that this property is not valid after removing any vector from $\Lambda_ {n,d}$. A number of properties of a typical graph of diameter $d$ is proved. In particular, it is obtained that such a graph for $d\geq 3$ does not possess the local $2$-diversity of balls and at the same time has the local $1$-diversity of balls, but has the full diversity of balls if $d=1,2$.
Ключевые слова:
graph, labeled graph, distance, metric ball, number of balls, diversity vector of balls, typical graph.
Поступила 5 мая 2016 г., опубликована 18 мая 2016 г.
Образец цитирования:
Т. И. Федоряева, “Строение вектора разнообразия шаров типичного графа заданного диаметра”, Сиб. электрон. матем. изв., 13 (2016), 375–387
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/semr682 https://www.mathnet.ru/rus/semr/v13/p375
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