Q42

MCQ2 marks, −0.67

Which of the properties hold for the adjacency matrix $A$ of a simple undirected unweighted graph having $n$ vertices?

(A)

The diagonal entries of $A^{2}$ are the degrees of the vertices of the graph.

(B)

If the graph is connected, then none of the entries of $A^{n-1} + I_{n}$ can be zero.

(C)

If the sum of all the elements of $A$ is at most $2(n-1),$ then the graph must be acyclic.

(D)

If there is at least a $1$ in each of $A\text{’s}$ rows and columns, then the graph must be connected.

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