Notation for two-vertex graph with m edges

Question

Is there standard notation for the graph on two vertices with $m$ edges between them?

Answer 1

Found an another (and arguably better) reference, which uses different notation. In Section 8.1.3 of Handbook of Discrete and Combinatorial Mathematics by Rosen, this graph is called the dipole graph (of size $m$) and denoted by $D_m$.

Answer 2

I think it is fairly standard to use $\lambda K_n$ to denote the complete multigraph (the graph on $n$ vertices, with $\lambda$ edges between every pair).

Answer 3

On page 578 of Graph Theory (Graduate Texts in Mathematics) by Bondy and Murty, this graph is called an $m$-bond and denoted by $B_m$.

Answer 4

A graph consists of two classes: The class of arrows (or edges) and the class of objects (or vertices) and two mappings from arrows to objects, called source and target(or domain and codomain).

Thus a graph may also be thought of as a functor $F$ from the category $ \space * \begin{matrix} \rightarrow\\ \rightarrow \end{matrix} *\space $ to $Sets$.

A graph with 2 vertices and m edges is then an above functor $F$ with $$|F(arrows)|=m$$ $$|F(objects)|=2$$