# Graph Theory - A Fun Field: Video Transcript

Bob Krueger [junior major in Mathematics; Physics, Class of 2019]: So, picture me senior year of high school. I knew I was coming to Miami the next year. I was over at a friend's house, and his brother was, as a matter of fact, a grad student here at Miami in math. So we got to chatting about math and Miami, and he told me to seek out Dr. [Louis] DeBiasio when I get there because that's who he did some work with, and he is just a nice guy, and so I should introduce myself and say hello.

Once I got to campus that first day, and they put all of the new freshmen in a room and introduced them to some of the math faculty, Dr. DeBiasio was there — and I'm gonna call him Dr. D from now on, because that's what everyone calls him — but Dr. D was there.

I told him about my experiences in high school and at some math camps and what I had done and asked if there were any classes that he suggest that I take or something along those lines, and he looked at me, and he said, "Hey, you really need to take this graph theory class."

So I went and talked to the professor that was teaching that that semester, eventually was able to talk my way into that, and started learning graph theory from then on, and graph theory was an interesting thing because I had learned a lot of math, and a lot of not just the typical calculus and linear algebra in high school, but some of the weirder, proofy-kind of math at these various camps and what-not.

Imagine, like, Facebook and all the friends that you have. Each of the friends are connected via, or each of the users on Facebook are connected via friendships — that is a graph. That's the sort of the things we study. Little nodes that are connected via these edges, and we study properties of those, whether they have, like, triangles in them, whether they have cycles of other sizes, and just whether we can color them in specific ways. It's sort of a fun field where you can just mess around with things. But it's interesting. It's very accessible to undergraduates and beginning math people as well, which is why it made for a good research project.

And so we started working on it. It was me, Dr. D, Dr. [Daniel] Pritikin, who taught my graph theory class first semester, and then another student named Eli [Thompson]. And it was all Dr. D's initiative.

You know, I mean it's obviously a huge influence as to what specific math I'm interested in. I never would've thought of graph theory — two years ago I would have thought of like set theory or logic, or one of those areas. But now it's something that I know a lot about and I know how to think about, is the biggest part. So it makes that interesting to me.

The whole process is just kind of serendipitous because like this only happened because I talked to him on the first day and introduced myself on that first day, and I only knew to talk to him because I had randomly met a grad student that went here. So it's just kind of crazy how those things happen. Sometimes you just have to step out of your comfort zone and just say hello and introduce yourself, and you never know what's going to come of it!

[April 2018]