My textbook gives the following definition "a graph $G=(V,E)$ consisting of $V$, a nonempty set of vertices and $E$, a set of edges. Each edge has either one or two vertices associated with it."
Now consider this "graph", o—, where o is a vertex and — is an edge. Is this a valid graph? If so, is it a subgraph of o—o ? (I know — is not valid because $V$ has to be nonempty)
(My textbook: "A subgraph of a graph $G=(V,E)$ is a graph $H=(W,V)$ where $W \subseteq V$ and $F \subseteq E$". My book also says "when edges and vertices are removed from a graph, without removing endpoints of any remaining edges, a smaller graph is obtained; such a graph is called a subgraph of the original graph")
What're the most "standard" definitions of graphs and subgraphs?