Most watermarking schemes for 3D meshes arise from the CAD community. The analysis of their watermarking performances are generally not easily tractable. In this paper, we describe a framework for fragile watermarking of 3D triangle meshes that enables accurate assessment of its performances. Experiments show the relevance of the method towards authentication and integrity of heritage data purposes. One often argues that authentication may be performed using pure cryptographic primitives. We use watermarking because we want to allow some non malicious transformations of the mesh. Moreover, our technique enables visual inspection of the mesh for integrity assessment. Our method is based on alteration of geometrical invariants along a special traversal of the mesh connectivity graph. We proove that our traversal takes linear time for maximizing the number of sites that can store a watermark bit. We deduce several watermarking properties of our scheme, including the minimum watermark segment (MWS), the security (in bits) of the embedding, the class of robustness and the probability of false alarm. To our knowledge, such an accurate characterization of a watermarking scheme for 3D triangle meshes is not trivial for other similar methods.