var caso1 = @"<p><br></p>";
var caso3 = @"<p><br><p>hola</p></p>";
Console.WriteLine(checaHtml(caso1));
Console.WriteLine(checaHtml(caso2));
Console.WriteLine(checaHtml(caso3));
public int checaHtml(string html) {
var htmlDoc = new HtmlDocument();
var elem = htmlDoc.DocumentNode.SelectNodes("p/br");