Can we give LDAP path Workgroup Name instead of Domain or IP Address

my code is below
string LdapPath="server09"; // server09 is workgroup name
string domainAndUsername = domain + @"\" + username;
entry = new DirectoryEntry(LdapPath, domainAndUsername, password);

try
{
entry.RefreshCache();// refreshing all attributes here
// Bind to the native AdsObject to force authentication.
// entry.AuthenticationType = AuthenticationTypes.SecureSocketsLayer;
Object obj = entry.NativeObject;
DirectorySearcher search = new DirectorySearcher(entry);
search.Filter = "(SAMAccountName=" + username + ")";
search.PropertiesToLoad.Add("cn");
SearchResult result = search.FindOne();
if (null == result)
{
return false;
}
// Update the new path to the user in the directory
LdapPath = result.Path;
string _filterAttribute = (String)result.Properties["cn"][0];


This Code is not working .Exception thrown by system "Server is not operational".