[net.math] The Null-Graph

weemba@brahms.BERKELEY.EDU (Matthew P. Wiener) (03/29/86)

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