# Computer Sciences

## Generation of colored graphs with isomorphism rejection

In the article we consider graphs whose vertices or edges are colored in a given number of colors — vertex and edge colorings. The study of colorings of graphs began in the middle of the 19th century, but the main attention is paid to proper colorings, in which the restriction applies that the colors of adjacent vertices or edges must be different. This paper considers colorings of graphs without any restrictions. We study the problem of generating all non-isomorphic vertex and edge $k$-colorings of a given graph without direct checking for isomorphism.

## Mathematical and computer simulation of the electrophysical properties of a multicellular structure exposed to nanosecond electrical pulses

The article presents mathematical and computer models which allow to study the electrophysical properties (permittivity, impedance) of a multicellular structure exposed to nanosecond electrical pulses. The paper proposes a simulation approach that includes complex use of the classical theory of describing the electrodynamic properties of dispersed systems and the effective medium theory. We describe cell geometry using Gielis equations, which allow us to take account of the irregular shapes of cell membranes.

## Imitation tools for automated systems used in small arms testing

Currently, various imitators (imitation tools) are widely used to test various equipment and evaluate its parameters. The main goal of developing new imitation tools in the field of creating automated systems used in testing small arms is to accelerate and cheapen the development and implementation of such systems. The article discusses the general structure of information-measuring systems used in testing small arms based on acoustic and optical blocking devices, as well as on the basis of a video camera.

## The construction of all nonisomorphic minimum vertex extensions of the graph by the method of canonical representatives

A graph $G = (V, \alpha)$ is called \textit{primitive} if there exists a natural $k$ such that between any pair of vertices of the graph $G$ there is a route of length $k$. This paper considers undirected graphs with exponent 2. A criterion for the primitivity of a graph with the exponent 2 and a necessary condition are proved. A graph is primitive with the exponent 2 if and only if its diameter is 1 or 2, and each of its edges is included in a triangle.

## Method of Markovian summation for study the repeated flow in queueing tandem M|GI|∞ → GI|∞

The paper presents a mathematical model of queueing tandem M|GI|∞ → GI|∞ with feedback. The service times at the first stage are independent and identically distributed (i.i.d.) with an arbitrary distribution function B1(x). Service times at the second stage are i.i.d. with an arbitrary distribution function B2(x). The problem is to determine the probability distribution of the number of repeated customers (r-flow) during fixed time period.

## Heavy outgoing call asymptotics for MMPP|M|1 retrial queue with two way communication and multiple types of outgoing calls

In this paper, we consider a single server retrial queue MMPP|M|1 with two way communication and multiple types of outgoing calls. Calls received by the system occupy the device for operating, if it is free, or are sent to orbit, where they make a random delay before the next attempt to occupy the device. The duration of the delay has an exponential distribution. The main issue of this model is an existence of various types of outgoing calls in the system. The intensity of outgoing calls is different for different types of outgoing calls.

## Output process of the M|GI|1 is an asymptotical renewal process

Most of the studies on models with retrials are devoted to the research of the number of applications in the system or in the source of repeated calls using asymptotic and numerical approaches or simulation. Although one of the main characteristics that determines the quality of the communication system is the number of applications served by the system per unit of time. Information on the characteristics of the output processes is of great practical interest, since the output process of one system may be incoming to another.

## Multi-criteria approach to pair-multiple linear regression models constructing

A pair-multiple linear regression model which is a synthesis of Deming regression and multiple linear regression model is considered. It is shown that with a change in the type of minimized distance, the pair-multiple regression model transforms smoothly from the pair model into the multiple linear regression model. In this case, pair-multiple regression models retain the ability to interpret the coefficients and predict the values of the explained variable.

## Asymptotic Analysis of the MMРР|M|1 Retrial Queue with Negative Calls under the Heavy Load Condition

In the paper, a single-server retrial queueing system with MMPP arrivals and an exponential law of the service time is studied. Unserviced calls go to an orbit and stay there during random time distributed exponentially, they access to the server according to a random multiple access protocol. In the system, a Poisson process of negative calls arrives, which delete servicing positive calls. The method of the asymptotic analysis under the heavy load condition for the system studying is proposed.

## Analysis of Closed Queueing Networks with Batch Service

We consider a closed queuing network with batch service and movements of customers in continuous time. Each node in the queueing network is an infinite capacity single server queueing system under a RANDOM discipline. Customers move among the nodes following a routing matrix. Customers are served in batches of a fixed size. If a number of customers in a node is less than the size, the server of the system is idle until the required number of customers arrive at the node. An arriving at a node customer is placed in the queue if the server is busy.