I am an undergraduate student, and I have authored a paper without the help of any advisor. The paper has been accepted in a conference. While listing the paper in my CV, should I include an advisor's name to show I am a "serious" researcher?

I think the key point here is that the paper has been accepted to a good conference. Either with or without your professor as a co-author, it is going to reflect well on you and add to your CV. Consider telling your advisor about the paper. If the camera-ready version has not been submitted, they might be able to give you valuable insights on how to improve the paper. I assume you are going to get a recommendation letter from them. Doing this will improve their opinion of you, and they will be able to talk about your work in the letter. Having a single author paper in a good conference is a plus for your application, but typically that is not the only thing admission committees are looking for. Recommendations are also an important (perhaps more important?) part of your application.

If you author the paper independently, you should *never* include the name of someone else in it.  It could be very bad if your adviser gets his name associated with the contents of a paper that he had no part in authoring or reviewing. You should mention that you worked with professor X.  You should mention that you authored a paper.  How the admissions committee views it depends on your letter of recommendations and statement of purpose, but it looks pretty good. The way that I'd cite something like this is (your name) (paper name) based on research conducted under the supervision of Z

I'm going to slightly disagree with the other answers. At least in my field of biology, a single-author paper from an unknown author will be viewed with deep skepticism. The reason is that it is surpassingly rare that no senior author played a part in experimental design and funding, and this kind of situation with only one author is typically seen when the student and advisor have had a serious falling-out and are basically no longer on speaking terms. With that in mind, you run the risk of seriously hurting your application; you'll show that you have scientific merit by dint of your paper having been accepted to a conference, but your application will have a black mark on it (unfairly) as you'll be seen as potentially difficult and hard to work with. However, you shouldn't lie and include an advisor's name who didn't actually have any role in your research - that kind of lie will be easily caught and destroy your chances of acceptance. Instead, you should make sure that your CV, letters of recommendation, and essay for your grad school app all explain why there is no senior author on your paper. You need a faculty member to vouch for your scientific merit and quell any of the initial skepticism a reviewer might have. This will allow the true impressiveness of your achievement to come through.

Was this advisor your research advisor ? If you did research with professor X but still wrote up and submitted the work independently; depending on your research area it might be standard practice to include the name of the professor who funded and/or oversaw the research. It would be ungrateful/unethical not to include their name. If this is truly your independent work, you don't need to add a co-authorship since you have already been accepted to a conference. An admissions committee is unlikely to look down on this and will in fact view it positively. However, it would help the admissions committee (since they maybe unfamiliar with your area of research) if one or more of your reference writers actually acknowledged your paper and explained its contributions clearly to the committee. This answer is based on what I know of grad school admissions in engineering. Assume that standards and culture are different in other departments, but I assume that "good" conference papers are not as common in biological sciences where only conference abstracts are the norm. The single biggest indicator of a good prospective PhD student is that they can be self-motivated and do good work independently. While non-engineering fields may have different reactions to a solely student authored paper, it reflects poorly on them if they are unable to view it positively.