### Abstract:

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With the rapid advances of the computer technology, Mathematics and Computer Science have developed into two entirely separate disciplines. Since graphical approach lend themselves naturally as model for a variety of situations, including the hardware of computer and certain aspects of computer software, Graph Theory plays an increasingly important role within Computer Science. In the study of graphs, it soon becomes evident that efficient algorithms are necessary for solving problems of any significant magnitude. It has become fashionable to mention that there are applications of Graph Theory to some areas of Physics, Chemistry, Computer technology, Electrical and civil engineering, Sociology and Economics.
Computers have made our daily activities easier with fast and highly accurate outcome. Since we find the applications of Graph Theory in almost all areas, using the computer to solve practical problems makes our task easy. Transforming of our problems into a form that can be understood by the computer is the task of a computer language. Algorithms are used for that purpose. This research consists of Algorithmic aspect of Trees in Graph Theory and is designed to emphasize the close tie between the theoretical and algorithmic aspect of Trees in Graph Theory. Rather than employing a specific computer language for presenting algorithms, the steps were used that are common to many languages. This research has introduced few algorithms, based on properties of Trees in Graph Theory, for practical problems which we often come across. A complexity analysis is also given for each algorithm.
The main objective is to recognize the algorithms to solve real world problems using the properties of Trees in Graph Theory and the other objective is to apply these algorithms to solve some problems in day to day life.