Аннотация
In this part of the paper non-oriented networks without loops are considered. A network $S$ consists of a set $U(n)$ of $n$ communication nodes and a set $H$ of nonoriented arcs $(u_i, u_j)$. For $U(n)$ the vector $A = (a_1, \dots, a_n)$ of nonnegative parameters $a_i$ is specified representing the information exchanged per time unit between the node $u_i$ and the other nodes of $U(n)$. For the arcs of $S$ a weight function is defined by $C(A) = \{c_{ij}\}$, where $c_{ii} = 0$ for all $i$. The set of all weight functions $C(A)$ is denoted by $\Gamma (A)$. The function $C(A)$ is called a $c$-realization of $A$ if $c_{ij} \le c$ for any $\text {arc} \in H$. A vector $A$ is said to be informational if $\Gamma (A) \ne \emptyset$ and it is called $c$-informational if there exists a $c$-realization $C(A) \in \Gamma (A)$.\par For the network $S$ the following results and properties are presented: necessary and sufficient conditions for $A$ to be informational (respectively-$c$-informational), an algorithm for constructing the $c$-realization $C(A)$, the minimum $c$ for which $A$ is $c$-informational and the general properties of all the $c$-realizations for a fixed $c$.
Ключевые слова
informational vector; $c$-realizations; non-oriented networks without loops
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