Simple Graphs Practice

(The instructions for using the applet are available on a separate page and can also be read under the first tab directly in the applet.)


This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet.

What if applet does not run?

(This applet was created to accompany Excursions in Modern Mathematics, Seventh Edition, by Peter Tannenbaum © Pearson Education. Reproduced with permission. An earlier version of the applet is still available online at

The sole purpose of the applet is to help accustom a student to the basic concepts of graph theory. A formal definition of graph is a combination of two sets V and E, where elements of V are termed vertices, while the elements of E are edges, and each consists of a pair of vertices from V. The two vertices in an edge may be equal, in which case the edge is called a loop. The number of times a vertex is included in the edges of a graph is called its degree. A vertex is incident to an edge if it's one of the two vertices in the pair (which is the edge.) An edge is incident to each of its constituent vertices. A loop incident to a vertex endows the vertex with two degrees.

A path in a graph between two vertices is a sequence of edges (a path), of which one is incident to the first vertex and another to the second, and which are incident in pairs to the same vertex. A path between two vertices is said to join them. If the two ends of the path coincide, the latter is called a circuit. A graph is connected if any two vertices can be joined by a path.

A vertex of odd degree is said to be odd; otherwise it's even.

A few very general properties of the graphs may be observed using the applet:

  1. The number of odd vertices is always even.
  2. For a connected graph, the number of odd vertices is either 0 or 2.
  3. The total degree of a graph equals double the number of edges.

More can be found on a separate page.

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