Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.3 4.3bsd-beta 6/6/85; site ucbvax.BERKELEY.EDU
Path: utzoo!watmath!clyde!cbosgd!hplabs!ucbvax!brahms!weemba
From: weemba@brahms.BERKELEY.EDU (Matthew P. Wiener)
Newsgroups: net.math
Subject: The Null-Graph
Message-ID: <12788@ucbvax.BERKELEY.EDU>
Date: Sat, 29-Mar-86 13:23:49 EST
Article-I.D.: ucbvax.12788
Posted: Sat Mar 29 13:23:49 1986
Date-Received: Sun, 30-Mar-86 10:45:15 EST
Sender: usenet@ucbvax.BERKELEY.EDU
Reply-To: weemba@brahms.BERKELEY.EDU (Matthew P. Wiener)
Organization: University of California, Berkeley
Lines: 38

I don't remember the reference for this paper by F Harary and
R C Read except that it was in a Springer Lecture Notes.  The
paper, while humorous, is serious.

I excerpt here from the beginning of their paper.

		IS THE NULL-GRAPH A POINTLESS CONCEPT?

			    ABSTRACT
	
	The graph with no points and no lines is discussed critically.
	Arguments for and against its official admittance as a graph
	are presented.  This is accompanied by an extensive survey of
	the literature.  Paradoxical properties of the null-graph are
	noted.  No conclusion is reached.

			 1.  INTRODUCTION

...
Some writers in graph theory ... have introduced to concept of a (or the)
"null-graph"--having no points and no lines; see Figure 1.
...
Note that it is not a question of whether the null-graph "really exists";
it is simply a question of whether there is any point in it.











			     Figure 1.

ucbvax!brahms!weemba	Matthew P Wiener/UCB Math Dept/Berkeley CA 94720