Which of the following statements regarding Bipartite Graphs are CORRECT?
$K_{4}$ contains $K_{3}$ (odd cycle of length 3), so $K_{4}$ is not bipartite. Statements 1, 2, 3 are correct.
Which of the following graph properties are invariant under Graph Isomorphism?
Isomorphic graphs share identical topological properties (vertices, edges, degree sequence). Memory layout is irrelevant.
Which of the following statements are TRUE regarding Strongly Connected Components (SCCs)?
All four statements are fundamental properties of SCCs and component DAGs.
Which of the following conditions guarantee the existence of an Eulerian Circuit in a connected graph?
Even degrees (undirected) and in-degree == out-degree (directed) guarantee Eulerian Circuits. Exactly 2 odd degrees gives an Eulerian Path, not circuit.
Which of the following representations are commonly used for Sparse Graphs (where E << $V^2)$?
Adjacency List, CSR, and Edge List consume O(V + E) space, ideal for sparse graphs. Full matrix takes O($V^2)$.