Hall–Janko graph
OK kiddo, imagine you have a piece of paper and some crayons. Now draw a bunch of dots on your paper and connect them with lines. That's called a graph.
The Hall-Janko graph is a very special kind of graph that has a lot of lines and dots, but it's not just random. It's actually very symmetrical and has some really cool properties.
You see, mathematicians used to think that certain kinds of graphs couldn't exist. But in the 1960s, a guy named Marshall Hall Jr. and another guy named Zvonimir Janko found a way to make one of those graphs!
The Hall-Janko graph has 100 vertices (that's just a fancy word for dots) and 506 edges (that's the lines that connect the dots). The vertices are arranged in a special pattern that makes the graph symmetrical.
But here's the really amazing thing about the Hall-Janko graph. It's what's called a "strongly regular graph." That means that every vertex has the same number of neighbors, and those neighbors are all connected in a certain way.
This might seem kind of boring, but it's actually really important in mathematics. Strongly regular graphs come up in all sorts of different areas, like coding theory and cryptography. So the Hall-Janko graph is really a star in the world of math!
The Hall-Janko graph is a very special kind of graph that has a lot of lines and dots, but it's not just random. It's actually very symmetrical and has some really cool properties.
You see, mathematicians used to think that certain kinds of graphs couldn't exist. But in the 1960s, a guy named Marshall Hall Jr. and another guy named Zvonimir Janko found a way to make one of those graphs!
The Hall-Janko graph has 100 vertices (that's just a fancy word for dots) and 506 edges (that's the lines that connect the dots). The vertices are arranged in a special pattern that makes the graph symmetrical.
But here's the really amazing thing about the Hall-Janko graph. It's what's called a "strongly regular graph." That means that every vertex has the same number of neighbors, and those neighbors are all connected in a certain way.
This might seem kind of boring, but it's actually really important in mathematics. Strongly regular graphs come up in all sorts of different areas, like coding theory and cryptography. So the Hall-Janko graph is really a star in the world of math!