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We study the single-site Glauber dynamics for the fugacity $\lambda$,Hard-core model on the random graph $G(n, d/n)$. We show that for the typicalinstances of the random graph $G(n,d/n)$ and for fugacity $\lambda <\frac{d^d}{(d-1)^{d+1}}$, the mixing time of Glauber dynamics is $n^{1 +O(1/\log \log n)}$.  Our result improves on the recent elegant algorithm in [Bezakova, Galanis,Goldberg Stefankovic; ICALP'22]. The algorithm there is a MCMC based samplingalgorithm, but it is not the Glauber dynamics. Our algorithm here is simpler,as we use the classic Glauber dynamics. Furthermore, the bounds on mixing timewe prove are smaller than those in Bezakova et al. paper, hence our algorithmis also faster.  The main challenge in our proof is handling vertices with unbounded degrees.We provide stronger results with regard the spectral independence via branchingvalues and show that the our Gibbs distributions satisfy the approximatetensorisation of the entropy. We conjecture that the bounds we have here areoptimal for $G(n,d/n)$.  As corollary of our analysis for the Hard-core model, we also get bounds onthe mixing time of the Glauber dynamics for the Monomer-dimer model on$G(n,d/n)$. The bounds we get for this model are slightly better than those wehave for the Hard-core model

On the Mixing Time of Glauber Dynamics for the Hard-core and Related Models on G(n,d/n)