In the article, using the criterion analysis method, the analysis of the stability of total costs, the sensitivity of parameters to changes in the initial data (to the analysis of the influence of errors in the initial data) is carried out, and recommendations are given on the use of the obtained parameters for 10 kV distribution electrical networks.

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Let $G=(V,E)$ be a finite graph. The Generalized Fan Graph $F_{m,n}$ is defined as the graph join $\overline{K_m}+P_n$, where $\overline{K_m}$ is the empty graph on $m$ vertices and $P_n$ is the path graph on $n$ vertices. Decomposition of Generalized Fan Graph denoted by $D(F_{m,n})$. A star with $3$ edges is called a claw $S_3$. In this paper, we discuss the decomposition of Generalized Fan Graph into claws, cycles and paths.

The article is devoted to modeling the gas-dynamic state of an elementary section of a gas pipeline during gas injection and its outflow through the choke in the final section of the pipe and to solving these problems using the method of characteristics. The subject of the study is the gas-dynamic state of an elementary horizontal section of a gas pipeline in the process of checking its serviceability for operation. The processes of gas injection into the section and gas outflow from it, considered in the article, were modeled using the N.E. Zhukovsky formula on gas outflow into unbounded space in a framework of the short pipeline approach. The original equations are linearized by introducing the mass flow rate of gas and waves traveling in two directions. When solving the problem, the method of characteristics was applied; numerical results were obtained and analyzed using an analytical solution to the problem. The research methods are based on the laws of conservation of momentum and gas mass, the d’Alembert method for solving a system of hyperbolic equations and the methods of conducting a computational experiment. An analytical solution to the problem with a rupture caused by an instantaneous change in the gas pressure at the end of the section is obtained. It is shown that the process proceeds with the formation of compression and rarefaction waves, and their multiple reflections at the ends of the section. The gas in the section tends to a state of rest with time, and the changes in the mass flow rate and gas pressure are of exponential nature.