Question

prove that a graph G with n vertices always has a hamiltonian path if the sum of the degree of every pair of vertices and Vi and Vj in G satisfies the condition d(Vi) +d(Vj) >=n-1​

Answer 1

Answer:

Step-by-step explanation:

A closed walk in a graph G containing all the edges of G is called an Euler line in G. A

graph containing an Euler line is called an Euler graph.

We know that a walk is always connected. Since the Euler line (which is a walk) contains

all the edges of the graph, an Euler graph is connected except for any isolated vertices the

graph may contain. As isolated vertices do not contribute anything to the understanding

of an Euler graph, it is assumed now onwards that Euler graphs do not have any isolated

vertices and are thus connected.