The Null-Graph

[Matthew P. Wiener]

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