Table of the largest known graphs of a given diameter and maximal degree
Okay kiddo, so you know what a graph is, right? It's a bunch of dots connected by lines. Well, sometimes people like to make really big graphs with lots and lots of dots and lines.
But, just like when you play connect the dots, the more dots you have, the more lines you need to connect them all. And that can make things really complicated and tangled up.
So, some smart people came up with a way to measure how complicated a graph is. They look at two things: the "diameter," which is the longest distance between any two dots, and the "maximal degree," which is the most lines that connect any one dot to other dots.
For example, if you made a graph with five dots and each dot had two lines connecting it to other dots, that would have a maximal degree of two. And if the longest distance between any two dots was three lines, that would have a diameter of three.
Now, these smart people made a table to keep track of the biggest graphs they knew about with a certain diameter and maximal degree. It's like a big chart with all the numbers and names of the graphs.
So, if you wanted to know what the biggest graph was that had a diameter of three and a maximal degree of four, you could look at the table and find the answer! Isn't that neat?
But, just like when you play connect the dots, the more dots you have, the more lines you need to connect them all. And that can make things really complicated and tangled up.
So, some smart people came up with a way to measure how complicated a graph is. They look at two things: the "diameter," which is the longest distance between any two dots, and the "maximal degree," which is the most lines that connect any one dot to other dots.
For example, if you made a graph with five dots and each dot had two lines connecting it to other dots, that would have a maximal degree of two. And if the longest distance between any two dots was three lines, that would have a diameter of three.
Now, these smart people made a table to keep track of the biggest graphs they knew about with a certain diameter and maximal degree. It's like a big chart with all the numbers and names of the graphs.
So, if you wanted to know what the biggest graph was that had a diameter of three and a maximal degree of four, you could look at the table and find the answer! Isn't that neat?