Mathematical Logic, Algebra, Number Theory and Discrete Mathematics

The absolute center of a graph in problems of optimal location of a mobile service center for technical systems

S. V. Ignatiev, Yu. A. Plaksa, S. A. Kurochkina, N. A. Prusova

Yaroslavl Higher Military School of Air Defense named after Marshal of the Soviet Union L.A. Govorov, Yaroslavl

Abstract: The problem of finding the optimal location of a mobile service center for technical systems is considered. The solution to this problem is based on the application of a minimax algorithm from graph theory. It is shown that the search for the optimal location of the mobile service center proceeds in several stages. The first stage involves a formalized description of the grouping of technical systems and obtaining a spatio-temporal model of the grouping, which consists of a multigraph and submatrices of reachability. At the second stage, the obtained multigraph is adapted for the use of the Hakimi method, and distance matrices are calculated. The third stage involves the search for local absolute centers of the graph and the computation of the absolute center of the graph. At the fourth stage, the location of the absolute center of the grouping of technical systems on the terrain is determined by approximating the route with a piecewise continuous temporal function.

Keywords: multigraph, reachability matrix, minimax algorithm, absolute center of a graph, Hakimi’s method, service center for technical systems.

UDC: 519.17

Received: 06.05.2025
Revised: 24.06.2025

DOI: 10.26456/vtpmk732

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