GATE CS 2021 : Discrete Math Quiz 6 (App update required to attempt this test)

Consider the two below given statements :

S1 : If G is a connected graph with degree sequence = {3,3,4,4,5,5} then the graph G is surely Hamiltonian graph.

S2 : If G is a connected graph with degree sequence = {2,2,3,3,4,5} then the graph G may or may not be Hamiltonian graph.

Which is correct ?

Consider a graph where its vertices are representing as n bit signal. 2 vertices are only connected with each other if their bit positions only differ by exactly 1 bit (n >= 2). Then the number of vertices?

Which of the following statement is true?

let G be a graph having 12 vertices and 3 components. The maximum number of edges in G is

If G is a forest with n vertices and k connected components, how many edges does G have?

If a graph of order 10 and size 15 with 3 components is given then find how many closed faces are there in the graph _________.