What is the balanced chemical equation for a redox reaction between a lithium-cobalt battery and a graphite electrode?
Below we have a simpler way of the $\ce{Li-Co}$ cell reactions.

Cathode half-reaction:

$$\ce{CoO2 + Li+ + e- &lt;=&gt; LiCoO2}$$

Anode half-reaction:

$$\ce{LiC6 &lt;=&gt; C6 + Li+ + e-}$$

Net-cell reaction:

$$\ce{LiC6 + CoO2 &lt;=&gt; C6 + LiCoO2}$$

Over-discharging supersaturates lithium cobalt oxide, leading to the production of lithium oxide.

$$\ce{Li+ + e- + LiCoO2 -&gt; Li2O + CoO}$$

Similarly overcharging (up to $\pu{5.2 V}$) leads to following reaction:

$$\ce{LiCoO2 -&gt; Li+ + CoO2 + e-}$$