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 semiedges, and isolated edges with two free ends, called free edges (Fiol and Vilaltella 2015).
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).
