denoted by $(\Lambda(G), \preceq)$. We make the poset $(\Lambda(G), \preceq)$ an edge labelled poset by assigning a positive integer to every edge of its Hasse diagram, such that if $\Lambda_k$ covers $\Lambda_j$ then the edge label on $\Lambda_j$-$\Lambda_k$ is $\displaystyle\binom{\Lambda_k}{\Lambda_j}$. We say that two edge labelled posets are isomorphic if they are isomorphic as posets, and there is an isomorphism between them that preserves the edge labels. This naturally leads to the notion of the [*abstract edge labelled poset*]{} of $G$: it is the isomorphism class of the edge labelled poset of $G$. Note that the notion of the abstract edge labelled poset of a graph is not to be confused with the isomorphism class of the Hasse diagram as a graph. An isomorphism from an edge labelled poset to itself is called an automorphism of the edge labelled poset. We denote the abstract edge labelled poset of $G$ by $\mathcal{ELP}(G)$. The Hasse diagram of the abstract edge labelled poset is simply the Hasse diagram of the edge labelled poset of $G$ with labels $\Lambda_i$ removed. The Hasse diagram of $\mathcal{ELP}(L_3)$ is shown in Figure 2.

\[fig-hasse\]

(600,1300) (300,100) (0,400) (300,400) (600,400) (0,700) (300,700) (600,700) (300,1000) (300,1300) (300,100)[(-1,1)[300]{}]{} (100,200)[2]{} (300,100)[(0,1)[300]{}]{} 