Prove that if G is a simple graph with |V (G)| = n even, where δ(G) ≥ n 2 + 1, then G has a 3-regular spanning subgraph.

Please discuss the following questions:
1)Why is Solomon v. Solomon & Co an important case?

2) What is the significance of a corporate veil in a business point of view?

Energy of a capacitor when dielectric is slowly pulled out but the battery is disconnected. Derive the expression: U=(1/8)E0A(1+k)^2 V^2

Question 1: a) The Salomon v Salomon [1897] case is the precedent for the doctrine of separate legal personality of a company. Explain the facts and the decision of the case and explain the reasons for the decision.

Hemoglobin and Myoglobin, HOW is oxygen binding regulated? what other mechanisms control oxygen binding in oxygenated vs deoxygenated tissues ( lung v. exercising muscles)?  

In every theme discuss one successful personality of Pakistan in detail i. Empathy ii. Ideation iii. Individualization iv. Strategic v. Responsibility vi. Include

Graph Theory

Prove:

If G is a graph for which deg(u)+deg(v) ≥n for each uv ∈EsubG, the G has a Hamiltonian cycle.

(with counter examples)

Verify the divergence theorem for the vector field F = 2xzi + yzj +z2k and V is the volume enclosed by the upper hemisphere x2 + y2 + z2 = a2, z ≥ 0