Abstract
Based upon Fermi 2FGL and 3FGL catalogues, a sample of 842 blazars (hereinto 356 FSRQs, 486 BL Lac objects) is collected to discuss the changes of $\gamma$ -ray photon spectral indices and brightness from 2FGL to 3FGL blazars. Our results indicate that the distributions of $\gamma$ -ray photon spectral indices and luminosities between 2FGL and 3FGL have no obvious difference; The photon spectral indices and $\gamma$ -ray luminosity from 2FGL are closely correlated with that from 3FGL respectively; There are close anti-relations between the change of photon spectral indices and the change of luminosity for FSRQs and BL Lac objects samples and for sub-class samples of HBLs, IBLs and LBLs, which suggests that the spectrum becomes flat when the source becomes bright.
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