GATE Computer Science (CS) 2022 Shift 1 Solved Paper

Question : 51 of 65

Marks: +1, -0

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

The diagonal entries of A2 are the degrees of the vertices of the graph.
If the graph is connected, then none of the entries of An-1 + In can be zero.
If the sum of all the elements of A is at most 2(n - 1), then the graph must be acyclic.
If there is at least a 1 in each of A’s rows and columns, then the graph must be connected.

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