# Application of Graph theory in Computer Science

#### Application of Graph theory in Computer Science

This paper on the graph theory is aiming at presenting what is considered to be the basic material, combined with broad variety of applications, to other branches of mathematics and also to the real world problems. An overview of two applications of graph theory are tackled within the scope of this paper in the context of computer science professionalism.

#### Relevance of graph theory to ad-hoc networks

This covers the discussion of the role the graph theory play in relation to the issues pertaining to the Mobile Adhoc Networks (MANETS). The Adhoc networks consider issues as routing, scalability, modelling the network, connectivity and simulation (Jajodia, 2013). The capability of the network being modeled as a graph, the analysis of these issues can be done through the model. Graphs are algebraically represented in form of matrices. Networks too can be automated through algorithms. Issues involving nodes mobility, node density, packet routing and link formations between the nodes have to be simulated. The simulation of these concepts uses the random graph theory. The issues of connectivity are analyzed by use of graph spanners. For instance, the initial introduction of a k-spanner graph or a k-spanner or a geometric spanner as a weighted graph over some sets of points as vertices with every pair of vertices being a path between them having the weight at most k times, and the spatial distance between the points, for a fixed value of k. another way of analyzing the connectivity issues is through sparsification, proximity graphs, and spectral graph theory. The proximity graphs are generally graphs in which the connection of the two vertices is done by an edge if and only if thevertices satisfy specific geometric requirements. There are also numerous algorithms available for the analysis of the congestion in MANET’swhere the modeling of these graphs is done on the basis of graph theoretical ideas.

#### Computer Network Security

The second application of the graph theory within the context of computer science is the algorithm of the graphs in computer network security. The vertex over algorithm recently have been used to slate the transmission of stealth worms on the large computer networks thereby designing optimal strategies to protect  the network from such types of virus attacks in real-time.

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