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Devon Vukovich '17

"Edge and Vertex Failure Games on Graphs"

Major/ Minor: Mathematics
Hometown: Bethlehem
Project Advisor(s):Dr. Nathan Shank

Briefly describe your project.

I worked as an undergraduate researcher for a REU hosted by Muhlenberg College. The REU was focused on working with the Online Encyclopedia of Integer Sequences. I worked as part of a Graph Theory research team that examined sequences that arose from the Edge Distinguishing Chromatic Number of different graph classes. I also worked as part of a Game Theory research team that expanded upon research done in component deletion games played on graphs.

Why did you decide to turn your idea into a SOAR project?

I had originally pitched an idea to my advisor to examine a connectivity parameter for graphs based on a partizan combinatorial game played on the graph. He referred me to apply for the REU seeing the opportunity for me not only gain background for my proposed project, but also to expose me to a more focused research environment and other areas of mathematical research that I had not previously considered.

How did your faculty advisor guide you through your research?

The benefits of working with my advisor are vast, but my favorite part of our collaborative work is ease with which we can communicate. My advisor and I have a good understanding of one another’s strengths, thought processes and capabilities. As such, we have very natural, comfortable and productive dialogues regarding my project.

What has been your biggest obstacle so far?

The largest obstacle I have faced is time constraints. This is not for lack of adequate time management, but the sheer volume of background, and supplemental learning that is necessary to navigate my project to meaningful results requires more time than could be afforded by the summer and following academic year.

What has been your biggest takeaway from this experience?

The biggest takeaway I have had is the understanding that it is not likely for me to ever “finish” my research. Not because of inability or some other obstacle, but because one cannot end that which has no end. Every result I obtain presents further questions, ideas and directions. The more I explore the greater I realize the depths to be. I look forward to continuing this research for what I anticipate to be the rest of my career.

What was the result of your project?

 I am not entirely sure how to summarize the results we obtained. We examined a variety of aspects such as changing the component of the graph that can be deleted, changing the structure of the graphs being played on, and comparing the original game to other known games to explore different game analysis techniques.

Will you expand on your research after this summer is over? If so, where would you like to see it go?

I am currently in the process of completing an Honors Project that is expanding upon my research. As I mentioned above, I would ultimately like to be able to develop a useful network connectivity parameter based on strategic modeling of the network.

In your own words, how do you feel about being awarded this opportunity? 

I am very happy that I was able to participate in SOAR. Further, I am without words to express the gratitude that I feel that I was able to expand my SOAR experience into an REU opportunity. Other students should take advantage of SOAR because with the right mindset and approach it can give you a very good example of not only working within a field of study, but doing it in a professional way. I feel more prepared for my future graduate studies because of the opportunities I had through SOAR.