On obtaining effective conditions for the solvability of a system of functional-differential equations determinated on a geometric graph

This paper is devoted to consideration of a boundary value problem for a system of functional differential equations determined on a geometric graph. The boundary conditions of the problem are determined by the conditions for the connection of the edges of the graph. There is an algorithm that reduces the system of equations on the graph to the system determined on the set $\Theta$ of disjoint segments of the real axis. The Azbelev's $W$-method is applied to the system determined on the set $\Theta,$ what makes it possible to obtain effective conditions for the unique solvability of the original system. An example is given.