I'm reading Saha Ray's book on graphs, there is a confusion point for me: on page 5:

Null graph: If E = Ø, in a graph G = (V, E), then such a graph without any edges is called a null graph.

on page 14:
Discrete graph: A graph is called discrete graph if E(G) = Ø.

Stable: X being a subset of V(G) is stable, if G[X] is a discrete graph.

wikipedia: In graph theory, an independent set or stable set is a set of vertices in a graph, no two of which are adjacent.

These bring me to the following conclusion:
- Discrete means null graph

Is the conclusion correct please?

  • $\begingroup$ From the definitions, it seems that the terms discrete graph and null graph are equivalent. I haven't heard the term "discrete graph" before though. Perhaps you mean "null graph" vs "empty graph" ? $\endgroup$ – Prasun Biswas Apr 10 '18 at 21:00
  • $\begingroup$ In the latter case, the distinction depends on the author. The term "empty graph" is used for graphs with $E(G)=\emptyset$ and "null graph" is used to refer particularly to the empty graph with $V(G)=\emptyset$; the terms are also sometimes interchangeably used. $\endgroup$ – Prasun Biswas Apr 10 '18 at 21:02

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