(a) Define a graph and explain the concepts of degree, path, cycle, and connectedness in an undirected graph: Differentiate between Eulerian and…

(a) Define a graph and explain the concepts of degree, path, cycle, and connectedness in an undirected graph: Differentiate between Eulerian and Hamiltonian graphs with examples.

(b) Explain the difference between Deterministic Finite Automata (DFA) and Non-Deterministic Finite Automata (NFA). Prove that for every NFA, there exists an equivalent DFA that recognizes the same language.

(c) Consider the following undirected weighted graph-

Vertices: A, B, C, D, E

Edges: (A-B)(4), (A-C)(2), (B-C)(1), (B-D)(5), (C-D)(8), (C-E)(10), (D-E)(2), (B-E)(6).

(i) Apply Dijkstra's algorithm to find the shortest path from vertex A to all other vertices.

(ii) Show the step-by-step table of distance updates, and

(iii) Determine the minimum distance from A to E.