Below are some more examples of graphs: Exercise 3. What is Graph Theory? Graph 8 is a directed graph. (In the figure below, the vertices are the numbered circles, and the edges join the vertices.) Draw four of your own graphs in the space below. Graph theory First thing that comes to your mind when somebody says ‘graph’ is probably some chart, pie chart, or a column chart maybe. Graph Theory - Types of Graphs. As used in graph theory, the term graph does not refer to data charts, such as line graphs or bar graphs. A graph consists of some points and some lines between them. Graph theory is the study of mathematical objects known as graphs, which consist of vertices (or nodes) connected by edges. If the graph carries that information with itself, it is called a directed graph. Other articles where Line graph is discussed: combinatorics: Characterization problems of graph theory: The line graph H of a graph G is a graph the vertices of which correspond to the edges of G, any two vertices of H being adjacent if and only if the corresponding edges of G are incident with the same vertex of G. Previous Page. We will discuss only a certain few important types of graphs in this chapter. Thus, the two graphs below are the same graph. In such a graph, an edge is drawn using an arrow instead of a line. Instead, it refers to a set of vertices (that is, points or nodes) and of edges (or lines) that connect the vertices. What if we told you that in a very similar way you can graph every function you know? A path in a graph that goes over each line exactly once is called an Euler Path. No attention is paid to the position of points and the length of the lines. There are various types of graphs depending upon the number of vertices, number of edges, interconnectivity, and their overall structure. All graphs in these notes are simple, unless stated otherwise. Graph Theory 1 You can simplify the problem by drawing a diagram with one point for every land mass and one line for every bridge: The above image is called a graph. A directed graph is also called a diagraph. Next Page . Graph theory concerns the relationship among lines and points. Advertisements. 2 Terminology, notation and introductory results The sets of vertices and edges of a graph Gwill be denoted V(G) and E(G), respectively. A basic graph of 3-Cycle. Any scenario in which one wishes to examine the structure of a network of connected objects is potentially a problem for graph theory. We have already met the complete graphs K v:1, while K v:2 is the complement of the line graph of K v . De nition 1. A simple graph is a nite undirected graph without loops and multiple edges. 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