A short note on undirected fitch graphs

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 xy ∈ 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.