Q. Which of these adjacency matrices represents a simple graph?

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Q. Given an adjacency matrix A = [ [0, 1, 1], [1, 0, 1], [1, 1, 0] ], how many ways are there in which a vertex can walk to itself using 2 edges.

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Q. If A[x+3][y+5] represents an adjacency matrix, which of these could be the value of x and y.

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Q. Two directed graphs(G and H) are isomorphic if and only if A=PBP-1, where P and A are adjacency matrices of G and H respectively.

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Q. Given the following adjacency matrix of a graph(G) determine the number of components in the G.

[0 1 1 0 0 0],

[1 0 1 0 0 0],

[1 1 0 0 0 0],

[0 0 0 0 1 0],

[0 0 0 1 0 0],

[0 0 0 0 0 0].

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Q. Incidence matrix and Adjacency matrix of a graph will always have same dimensions?

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Q. The column sum in an incidence matrix for a simple graph is __________

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Q. What are the dimensions of an incidence matrix?

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Q. The column sum in an incidence matrix for a directed graph having no self loop is __________

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Q. Time complexity to check if an edge exists between two vertices would be ___________

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Q. The graphs G1 and G2 with their incidences matrices given are Isomorphic.

e1 e2 e3 e4 e5 e6
v1 1 0 0 0 0 0
v2 1 1 0 0 0 1
v3 0 1 1 0 1 0
v4 0 0 1 1 0 0
v5 0 0 0 1 1 1



e1 e2 e3 e4 e5 e6
v1 0 0 1 0 0 0
v2 1 0 1 0 1 0
v3 1 1 0 1 0 0
v4 0 1 0 0 0 1
v5 0 0 0 1 1 1

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Q. If a connected Graph (G) contains n vertices what would be the rank of its incidence matrix?

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Q. A Graph Structured Stack is a _____________

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Q. If a Graph Structured Stack contains {1,2,3,4} {1,5,3,4} {1,6,7,4} and {8,9,7,4}, what would be the source and sink vertices of the DAC?

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Q. Graph Structured Stack finds its application in _____________

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Q. If in a DAG N sink vertices and M source vertices exists, then the number of possible stacks in the Graph Structured Stack representation would come out to be N*M.

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Q. Space complexity for an adjacency list of an undirected graph having large values of V (vertices) and E (edges) is ___________

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Q. For some sparse graph an adjacency list is more space efficient against an adjacency matrix.

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Q. Time complexity to find if there is an edge between 2 particular vertices is _________

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Q. For the given conditions, which of the following is in the correct order of increasing space requirement?
i) Undirected, no weight

ii) Directed, no weight

iii) Directed, weighted

iv) Undirected, weighted

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