Complete Graph
A complete graph is a graph, which has edges connecting all pairs of vertices.
Essential Further Mathematics 4ed 2012 (page 624)
*In the above diagram, only K5 is a complete.
To work out the number of edges a complete graph will have, the vertices can be used to work that out using this formula:
where ‘n’ is equal to the number of vertices.
In order to determine whether a graph is complete, from an adjacency matrix one key feature to look for in the matrix is a row of 0s in the diagonal, with 1s filling the rest of the matrix.
Essential Further Mathematics 4ed 2012 (page 624)
Feedback
Want to suggest an edit? Have some questions? General comments? Let us know how we can make this resource more useful to you.
More Resources
VCAA Pages
Useful Sites
Revision Resources
The Engage Wiki is a free resource provided by the Engage Education Foundation. Unless otherwise noted, all content is copyright © 2023 Engage Education Foundation. All rights reserved.
While we endeavour to provide you with great study material - we’re not qualified teachers, as such Engage cannot guarantee the validity of the information here.
The Victorian Curriculum and Assessment Authority (VCAA) does not endorse this website and makes no warranties regarding the correctness or accuracy of its content. VCE is a registered trademark of the VCAA. Current and past VCE exams and related content can be accessed directly at www.vcaa.vic.edu.au