Regular graph
A regular graph is an undirected graph whose vertices all have the same degree. In particular, an undirected graph is considered to be \(k\)-regular if all its vertices have exactly \(k\) neighbors.
An undirected graph \(G = (V, E)\) is \(k\)-regular if and only if for every vertex \(v \in V\):
$$\text{deg}(v) = k$$
⚠ No exceptions allowed! If even a single vertex has a different degree, the graph is not regular.
Logic & Proofs
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Set Theory
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