Graph Theory

Question

Which of the following statements is incorrect
i) In a graph G with number of vertices n, n ≥ 2, there are two vertices that have exactly the same degree
ii) Let G be a K-regular bipartite graph with k ≥ 2. Then G has no cut edge

Comments

i -true

ii - false

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i think both the statements are true .

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In K-regular graph all vertices of one side is connected to other side vertices.

i think, removal of one edge  graph is not disconnected.(more than one component in previous graph)

Answer 1

1. nothng is mentioned about the type of graph , so can't comment accurately, otherwise considering the Simple Graph the statment is True that atleast 2 vertex must have same degree (Havell-Hakimi theorem).

2. Statment True: because as k>=2 there cant be any edge whose removal disconnect as every vertex has same degree and being bipartite 2 sets willalways be connected even though 1 edge is removed