# Graph theory teaching materials for young students

Does anyone have any good sources to teach upper primary so grade 7 students basics on graph theory? The only ones I can find are for like upper middle school and high school, and having trouble finding friendly sources for grade 7 students. I would appreciate the sources if any is provided.

• This is intended for younger students but might be useful. Commented Aug 30, 2019 at 11:32
• Dots and Lines or Introduction to graph theory by Richard Trudeau is inexpensive and good enough for an intro book: amazon.com/Introduction-Graph-Theory-Dover-Mathematics/dp/… It is dense, so read sequentially in short portions, do not skip sections. Commented Aug 30, 2019 at 18:43
• @RustyCore Post an answer so I can upvote it! Commented Aug 30, 2019 at 23:38
• Grade 7 and "upper middle school" seem very close to me. I'm curious what you found for "upper middle school and high school" that wouldn't be good for 7th grade? Commented Aug 31, 2019 at 15:02
• This is apparently for younger kids, but maybe some of it will be useful: jdh.hamkins.org/math-for-eight-year-olds/… Commented Sep 8, 2019 at 19:51

One of the charms of graph theory is that people of all ages often enjoy learning graph theory ideas and tools. One place one can read about these ideas is in the book called For All Practical Purposes (I am a co-author) which has gone through 10 editions. The book was designed for college liberal arts students who might have almost no proficiency with algebra. However, "brave" 5th graders and above can read the beginning chapters, which treat graph theory related ideas.

Unfortunately, many treatments of basic graph theory don't use applications settings as a carrot to interest beginners. Thus, while the historical roots of graph theory are often tied to Euler's work on a recreational mathematics problem involving the traversal of bridges, a much more natural collection of settings for Euler's work relates to operations research—finding an efficient route for a pot-hole inspector, a snow plow, mail delivery, or distributing advertising flyers. The beautiful theorem is that a graph in one piece has a tour starting at any vertex and finishing at the same vertex which traverses each edge once and only once if and only if the graph has an even number of local line segments (edges) at a vertex. Few "real world" graphs have this property but one can modify the applied and theoretical questions so as to look for the tour which minimizes the number of repeated edges or minimizes the total weight of the tour (where each edge has some positive weight, time or cost attached to it). This approach leads to the beautiful "model" often called the "Chinese postman problem."

Other nifty applied graph theory problems lead to questions which relate to hamiltonian circuits in graphs, coloring the vertices, edges or faces of a graph, or finding matchings of different kinds in a graph.

The important point for me is that applications settings and appealing geometric diagrams quickly lead to nifty theory (the proof of the theorem mentioned above is very intuitively appealing) that can "hook" lower grade students (or adults) who might not find "algebra" based mathematics as having the "charm" that graph theory mathematics does for many.

• 'can "hook" lower grade students': Yes! Commented Aug 31, 2019 at 1:04
• +1: I use For All Practical Purposes to teach a course for non-science students at a liberal arts college, and we spend some time on the graph theory section. Commented Sep 6, 2019 at 2:02

Here are GeoGebra materials: Graph Theory for Kids, inspired by Joel Hamkins' notes, to which @A.Goodier pointed.

Four-color challenge.

If you're also interested in Network Science more broadly than Graph Theory, there is this list of "Network Literacy: Essential Concepts and Core Ideas" from the NSF-sponsored Network Science in Education group.

• Welcome to matheducators.SE. Could you describe the contents of the link briefly to improve your answer? Commented Sep 8, 2019 at 11:00
• @Leo Answers that are only links will be deleted eventually as "not an answer." I hope you have time to add to this answer, or, if you are seeing this notification after the answer is deleted, I hope you will come back and write more about it. Thanks! Commented Sep 9, 2019 at 16:24
• With apologies for the bad answer, I wanted to thank you all for pointing it out and to @kcrisman for editing the answer.
– Leo
Commented Sep 10, 2019 at 2:02
• @Leo if you could actually list the concepts and edit your answer accordingly, that would be great; unfortunately they don't seem to be easy to cut and paste from the document they link to :( but that would make the answer much more useful. Commented Sep 10, 2019 at 2:10