We pursue an account of merging through the use of geodesic semantics, the semantics based on the length of the shortest path on a graph. This approach has been fruitful in other areas of belief change such as revision and update. To this end, we introduce three binary merging operators of propositions deﬁned on the graph of their valuations and we characterize them with a ﬁnite set of postulates. We also consider a revision operator deﬁned in the extended language of pairs of propositions. This extension allows us to express all merging operators through the set of revision postulates.