The synchrotron external shock model predicts the evolution of the spectral (β) and temporal (α) indices during the gammaray burst (GRB) afterglow for different environmental density profiles, electron spectral indices, electron cooling regimes, and regions of the spectrum. We study the relationship between α and β, the so-called "closure relations" with GRBs detected by Fermi Large Area Telescope (Fermi-LAT) from 2008 August to 2018 August. The spectral and temporal indices for the > 100 MeV emission from the Fermi-LAT as determined in the Second Fermi-LAT Gamma-ray Burst Catalog (2FLGC; Ajello et al. 2019) are used in this work. We select GRBs whose spectral and temporal indices are well constrained (58 long-duration GRBs and 1 short-duration GRBs) and classify each GRB into the best-matched relation. As a result, we found that a number of GRBs require a very small fraction of the total energy density contained in the magnetic field ( B 10 −7 ). The estimated mean and standard deviation of electron spectral index p are 2.40 and 0.44, respectively. The GRBs satisfying a closure relation of the slow cooling tend to have a softer p value compared to those of the fast cooling. Moreover, the Kolmogorov-Smirnov test of the two p distributions from the fast and slow coolings rejects a hypothesis that the two distributions are drawn from the single reference distribution with a significance of 3.2 σ. Lastly, the uniform density medium is preferred over the medium that decreases like the inverse of distance squared for long-duration GRBs. 1 the ratio of total counts between two energy bands; e.g., 50-100 keV and 100-300 keV 2 the time during which the cumulative background-subtracted counts increase from 5% to 95%