I can list at least four reasons, related to files at this website:
- I argue that Kids & Teens need "Mathematical DNA", constucted from four "Mathematical Amino Acids": ARITHMETIC, TOPOLOGY, COMBINATORICS, GROUP THEORY. Graph Theory straddles the middle two of these.
- I argue the "The Black Hole in Education" is failure -- in a Democracy and a Market Economy -- to TEACH or TEST for COMBINATORICS: THE MATHEMATICS OF CHOICE.
- I wish young people to know that: YOU ARE THE DECISIONS YOU CAN MAKE AND THE ROLES YOU CAN PLAY.
- And I wish them to know that -- even on an earth with limited material resources -- each of us is vastly rich in our CHOICES, as I show in "Building a Google World in a Shoebox".
Graph theory is a vast field of modern mathematics. It is primarily taught and used in the sense of COMBINATORICS ("theory of choices"), elsewhere treated in "Mathematical DNA".A GRAPH is a 2D structure composed of a set of vertices ("corners") called NODES, two or more of which may be linked by "connectors" called EDGES. If each NODE has at least two EDGES, the GRAPH is CONNECTED, otherwise partially or totally DISCONNECTED or UNCONNECTED -- as in a TREE. EDGES can be UNDIRECTED or DIRECTED. If only one EDGE connects to each NODE, the GRAPH is SIMPLE.
Graphs are also UNDIRECTED or DIRECTED, UNLABELED OR LABELED. And we care also about ODDNESS/EVENNESS OF NODES.
The spools and rods of TINKERTOY are "ideal" for modeling GRAFS. Kids put together structures, usually 3D, such as "towers", "houses", "animals", "ferris wheels", "airplanes", etc. 2D structures are rare or absent in play with a Tinkertoy set.
Many applications of these GRAPHS are "pathways" of STRUCTURE or of PROCESS, hence, my term, "TRAFGRAF" for "traffic-graph".
Kids hear enough on TV about pharmaceutical drugs and chemical compounds and biological structures (such as DNA), as well as trafficpatterns, that they can be assured that "the world is full of TRAFGRAFS" and MOTIVATED into ACTIVITY, with "seeds planted for future gathering".