The shortest path algorithm is one of the best choices for implementation of data structures. The shortest path (SP) problem involves the problem of finding a suitable path between “two vertices or nodes in a graph” in such a way that the sum of the weights of its component edges is minimal. There are many theories for solving this problem one of the widely used way solution for solving this problem is Dijkstra’s algorithm (DA) which is also widely used in many engineering calculation works also. There are two types of DA one is the basic one and other one is optimized. This paper is focused on the basics one which provides a shortest route between source node and the destination node. Main focus has been kept on keeping the work simple and easy to understand with some basic concepts .Storage space and operational efficiency improvement has been tried to improve.

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In this paper we introduce the Max-Min intuitionistic fuzzy matrix M (G) of an intuitionistic fuzzy graph. And the extreme energy of M (G) is defined. And also we give the explicit expression for the coefficients of the characteristic polynomial of M (G) . These concepts are illustrated with real time example.

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