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Graph theory is rapidly moving into the main stream of research because of its applications in diverse fields such as biochemistry (genomics), coding theory, communication networks and their security etc. In particular researchers are exploring the concepts of graph theory that can be used in different areas of Cryptography. In this paper a review of the works carried out in the field of Cryptography which use the concepts of Graph Theory, is given. Some of the Cryptographic Algorithms based on general graph theory concepts, Extremal Graph Theory and Expander Graphs are analyzed.

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In recent times, Unmanned Air Vehicles (UAVs) are being deployed for several tasks of terrain coverage such as surveillance, photogrammetry, smart irrigation, civil security, and disaster management. In these applications, one of the most vital issues to be addressed is, covering the area under observation with minimum traversal for the UAV. So, the problem addressed in this paper is as follows: For a given geographic area and the given parameters describing the UAV’s coverage capacity, the problem is to find an optimal route that covers the given geographic area. In this paper, an optimal path planning algorithm for the area under observation, given as a closed curve, is proposed. The algorithm partitions the given area of interest into multiple non-uniform rectangles while considering other parameters such as the flying altitude of the UAV and obstacles that could be encountered during its flight. The problem is transformed into Traveling Salesman Problem by constructing a graph from the rectangular partitioning. Effective approximate solutions are provided to this problem, using the Minimum Spanning Tree (MST) approximation algorithm and Ant Colony Optimization (ACO). The experimental results show that ACO outperforms the MST based algorithm as it does not get stuck in local minima.