- - - Department of Mathematics, Izmir University of Economics, Izmir ۳۵۳۳۰, Turkey
- - - Department of Software Engineering, Manisa Celal Bayar University, Manisa ۴۵۴۰۰, Turkey
- - - Department of Mathematics, Manisa Celal Bayar University, Manisa ۴۵۱۴۰, Turkey

In this study, we introduce a novel hybrid method based on a simple graph along with operational matrix to solve the combined functional neutral differential equations with several delays. The matrix relations of the matching polynomials of complete and path graphs are employed in the matrix-collocation method. We improve the obtained solutions via an error analysis technique. The oscillation of them on time interval is also estimated by coupling the method with Laplace-Pad\'{e} technique. We develop a general computer program and so we can efficiently monitor the precision of the method. We investigate a convergence rate of the method by constructing a formula based on the residual function. Eventually, an algorithm is described to show the easiness of the method.

Collocation points, Graph theory, Laplace-Padé method, Matching polynomial, Vulnerability