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Graph Theory - Comprehensive Reference Guide
In the domain of mathematics and computer science, graph theory is the study of graphs that concerns with the relationship among edges and vertices. It is a popular subject having its applications in computer science, information technology, biosciences, mathematics, and linguistics to name a few. Without further ado, let us start with defining a graph.
The list of topics mentioned in this application is as follows: fundamentals related information, basic properties related information, types of graphs related information, trees related information, connectivity related information, coverings related information, matchings related information, independent sets related information, coloring related information, isomorphism related information, traversability related information, examples related information
a graph is a pictorial representation of a set of objects where some pairs of objects are connected by links. the interconnected objects are represented by points termed as vertices, and the links that connect the vertices are called edges.
Graph theory has its applications in diverse fields of engineering −
Electrical Engineering − The concepts of graph theory is used extensively in designing circuit connections. The types or organization of connections are named as topologies. Some examples for topologies are star, bridge, series, and parallel topologies.
Computer Science − Graph theory is used for the study of algorithms. For example,Kruskal's Algorithm,Prim's Algorithm,Dijkstra's Algorithm
Computer Network − The relationships among interconnected computers in the network follows the principles of graph theory.
Science − The molecular structure and chemical structure of a substance, the DNA structure of an organism, etc., are represented by graphs.
Linguistics − The parsing tree of a language and grammar of a language uses graphs.
General − Routes between the cities can be represented using graphs. Depicting hierarchical ordered information such as family tree can be used as a special type of graph called tree.
A graph is a diagram of points and lines connected to the points. It has at least one line joining a set of two vertices with no vertex connecting itself. The concept of graphs in graph theory stands up on some basic terms such as point, line, vertex, edge, degree of vertices, properties of graphs, etc.
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