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GATE | CS 2022 | Question 52

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

(A)

The diagonal entries of A2 are the degrees of the vertices of the graph. 

(B)

If the graph is connected, then none of the entries of An-1 + In 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’s rows and columns, then the graph must be connected. 


Answer: (A)

Explanation:

A2 diagonal elements

= (1.1 or 0.0) + (1.1 or 0.0) + ….. + (1.1 or 0.0) [ for n times ]

let some specific node C, if C – A edge present, then 1.1 instead of 0.0 with respect to node A in the above equation

therefore for each edge between C and Vertex, there should be one 1 in the above equation.

Therefore A2 diagonal elements = degree of the vertices of the graph.


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Last Updated : 12 Mar, 2022
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