how to find whether user is logged out from facebook or not using c# facebook api?

Its not possible with the facebook C# API. As long as your application has the access token to the facebook and facebook responds to the requests with this access token, the user is logged into the facebook.

The alternative way is using javascript

<div id="fb-root">

<script type="text/javascript" language="javascript">

window.onload=function()

{

// initialize the library with your Facebook API key

FB.init({ apiKey: 'b65c1efa72f570xxxxxxxxxxxxxxxxx' });

// fetch the status 

// you must have the login status before you can logout

// and if you authenticated via oAuth (server side), this is necessary.

// if you logged in via the JavaScript SDK, you can simply call FB.logout()

// once the login status is fetched, call handleSessionResponse

FB.getLoginStatus(handleSessionResponse);

}

// handle a session response from any of the auth related calls

function handleSessionResponse(response) {

// if we dont have a session (which means the user has been logged out, redirect the user)

if (!response.session) {

window.location = "/mysite/Login.aspx";

return;

}

}

</script>
</div>

More info here http://facebooksdk.blogspot.com/2011/06/facebook-logout.html