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If I were to apply to a Ph.D. program for mathematics and in the application mentioned that my intended field of study would be something in algebra, would the admissions committee be interested in a paper on graph theory that I wrote and gave a talk about at an AMS conference for undergraduate research?

I think I did some good work (for an undergraduate), but I don't know if application reviewers would value work in graph theory for somebody looking to go into an algebra related field. If it matters at all, the paper was on various forms of dominating sets.

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Yes, a graph theory paper is just as relevant as an algebra paper for graduate admissions, even if you plan to specialize in algebra. There are several reasons for this:

  1. Many people applying to math graduate school don't really know what they will specialize in. (This is true even for the very strongest applicants.) It's OK not to know, and everyone realizes that you may change your mind in a year or two even if you think you know now.

  2. Undergraduate research is generally limited by the availability of supervision. You may not have had the opportunity to work on your favorite topic.

  3. Undergraduate research is not intended as a head start for graduate school. Even if you had written an algebra paper, you would almost certainly not end up building on that work for your Ph.D. thesis. Instead, the real purposes are learning about research and demonstrating your talents, and the research topic itself is not so important.

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