Right: X-ray to bolometric luminosity ratios of M 34 sample stars vs. Rossby numbers. The solid line represents the rotation-activity relationship derived by Wright et al. (2011), and the dashed line represents the X-ray evolution model set-up in the present study based on M 34 data. Left: X-ray luminosities vs. rotation periods of M 34 stars compared with this X-ray evolution model for stellar masses in the range 0.4 ≤ M/M_⊙ ≤ 1.2. In both graphs, M 34 stars represented as red squares belong to the C sequence. M 34 stars represented as blue circles are members of the I sequence. Triangles represent M 34 gap stars assumed to be evolving from the C sequence towards the I sequence.