A graph multipole, or simply a multipole in graph theory, is a graph-like object obtained by cutting some edges of a cubic graph. The resulting object may have dangling edges with one free end, called a semiedge, and isolated edges with two free ends, called free edges (Fiol and Vilaltella 2015).
The semiedges may be partitioned into sets called connectors. A graph multipole with exactly two connectors is called a graph dipole (Máčajová and Škoviera 2021), not to be confused with a dipole graph.
Graph multipoles are used in the study of snarks. A 3-edge coloring of a graph multipole induces a coloring, or state, of its semiedges, and these states satisfy the parity lemma (Fiol and Vilaltella 2015).
