Teaching UGC NET Mock Test Series 2025 (Paper 1 & 2) Engineering Mathematics Graph Theory Connectivity
If a graph (G) has no loops or parallel edges and if the number of vertices(n) in the graph is n≥3, then the graph G is Hamiltonian if
(i) deg(v) ≥n/3 for each vertex v
(ii) deg(v) + deg(w) ≥ n whenever v and w are not connected by an edge.
(iii) E (G) ≥ 1/3 (n - 1)(n - 2) + 21
(i) and (iii) only
2
(ii) and (iii) only
3
(iii) only
4
(ii) only