# A short note on undirected Fitch graphs

### Abstract

Fitch graphs have been introduced as a model of xenology relationships in phylogenomics. Directed Fitch graphs *G* = (*X*, *E*) are di-graphs that are explained by {0, 1}-edge-labeled rooted trees with leaf set *X*: there is an arc *x**y* ∈ *E* if and only if the unique path in *T* that connects the least common ancestor lca(*x*, *y*) of *x* and *y* with *y* contains at least one edge with label 1. In this contribution, we consider the undirected version of Fitch’s xenology relation, in which *x* and *y* are xenologs if and only if the unique path between *x* and *y* in *T* contains an edge with label 1. We show that symmetric Fitch relations coincide with class of complete multipartite graph and thus cannot convey any non-trivial phylogenetic information.