Hossein Jafari - Young Researchers and Elite Club, Arak Branch, Islamic Azad University, Arak, Iran.
Setareh Salehfard - Department of Computer Science, Arak Branch, Islamic Azad University, Arak, Iran.
Dariush Aqababaei Dehkordi - Department of Mathematics, Shahrekord university, shahrekord, Iran.

The problem of path detection in graphs has been proposed from the past up to present, and various solutions have been proposed for this purpose, but it is often not an easy task to implement these methods on a computer. In this paper, a technique for detecting paths in a graph will be introduced using matrix algebra, which makes it possible to implement this rule on a computer. This method can be helpful the optimization of tree-spanning trees in networks. At the end of this study, a numerical example is solved using the proposed method.

Discrete Mathematics, Optimization, Path Design, Graph Theory