<p>We present a scheme for the thermal entanglement and teleportation fidelity of two electrons in the half-filled Hubbard model of the graphene honeycomb lattices. The analytical thermal entanglement, the teleportation fidelity and the average teleportation fidelity expressions are obtained. The effects of the temperature, the on-site repulsion and the nearest-neighbor interaction on the Concurrence, the teleportation fidelity and the average teleportation fidelity are discussed in detail. The findings suggest that weaker or stronger values of the on-site repulsion, the nearest-neighbor interaction will diminish quantum correlations and teleportation fidelity in the system. Furthermore, the average fidelity <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4767_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathcal {F}}_A \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">F</mi> <mi>A</mi> </msub> </math></EquationSource> </InlineEquation> of teleportation using thermal entangled state is confined in the inequality <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4767_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="118" /> </InlineMediaObject> <EquationSource Format="TEX">\(1 / 4 \le {\mathcal {F}}_A \le 1 / 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo stretchy="false">/</mo> <mn>4</mn> <mo>≤</mo> <msub> <mi mathvariant="script">F</mi> <mi>A</mi> </msub> <mo>≤</mo> <mn>1</mn> <mo stretchy="false">/</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>. These investigation have significant implications for quantum physics and its practical applications in quantum information processing.</p>