  The nature of the shallow decay phase in the X-ray afterglow of the gamma-ray
burst (GRB) is not yet clarified. We analyze the data of early X-ray afterglows
of 26 GRBs triggered by Burst Alert Telescope onboard Neil Gehrels Swift
Observatory and subsequently detected by Fermi Large Area Telescope (LAT)
and/or Imaging Atmospheric Cherenkov Telescopes. It is found that 9 events
(including 2 out of 3 very-high-energy gamma-ray events) have no shallow decay
phase and that their X-ray afterglow light curves are well described by single
power-law model except for the jet break at later epoch. The rest are fitted by
double power-law model and have a break in the early epoch (around ks),
however, 8 events (including a very-high-energy gamma-ray event) have the
pre-break decay index larger than 0.7. We also analyze the data of well-sampled
X-ray afterglows of GRBs without LAT detection, and compare their decay
properties with those of high-energy and very-high-energy gamma-ray events. It
is found that for the GeV/TeV bursts, the fraction of events whose X-ray
afterglows are described by single power-law is significantly larger than those
for non GeV/TeV GRBs. Even if the GeV/TeV GRBs have shallow decay phase, their
decay slope tends to be steeper than non GeV/TeV bursts, that is, they have
less noticeable shallow decay phase in the early X-ray afterglow. A possible
interpretation along with the energy injection model is briefly discussed.
