Centaurus A (Cen~A) is the nearest active radio galaxy, which has kiloparsec (kpc) scale jets and {giant lobes detected by various instruments in radio and X-ray frequency ranges}. The $Fermi$--Large Area Telescope and High Energy Stereoscopic System (HESS) confirmed, that Cen~A is a very high-energy (VHE; $> 0.1$~TeV) $gamma$-ray emitter with a known spectral {softening} in the energy range from a few GeV to TeV. In this work, we consider a synchrotron self-Compton model in the nucleus for the broad band spectrum {below the break energy} and an external Compton model in kpc-scale jets for the $gamma$-ray excess. Our results show that the observed $gamma$-ray excess can be suitably described by the inverse Compton scattering of the starlight photons in the kpc-scale jets, which is consistent with the recent tentative report by the HESS on the spatial extension of the TeV emission along the jets. Considering the spectral fitting results, the excess can only be seen in Cen~A, which is probably due to two factors: (1) the host galaxy is approximately 50 times more luminous than other typical radio galaxies and (2) the core $gamma$-ray spectrum quickly decays above a few MeV due to the low maximum electron Lorentz factor of $gamma_{rm c}=2.8 times 10^3$ resulting from the large magnetic field of 3.8~G in the core. By the comparison with other $gamma$-ray detected radio galaxies, we found that the magnetic field strength of relativistic jets scales with the distance from the central black holes $d$ with $B (d) propto d^{-0.88 pm 0.14}$.
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