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Standard VII

Mathematics

Faces, Edges and Vertices

A directed gr...

Question

A directed graph with an vertices and e edges are represented by adjancy matrix. What is the time required to determine the in-degree of a vertex?

0

(e)

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0

(n)

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0 (n^{2})

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0

(e + n)

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Solution

The correct option is D $0$ (n)

A directed graph with an vertices and e edges are represented by adjacency matrix. 0(n) is the time required to determine the in-degree of a vertex.

A directed graph is a set of vertices and a collection of directed edges that each connects an ordered pair of vertices. We say that a directed edge points from the first vertex in the pair and points to the second vertex in the pair.

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Similar questions

Q. A sink in a directed graph is a vertex i such that there is an edge from every vertex j

\neq

i to i and there is no edge form i to any other vertex. A directed graph G with n vertices is represented by its adjacency matrix A, where A[i] [j] = 1 if there is an edge directed from vertex i to j and 0 otherwise.

The following algorithm determines whether there is a sink in the graph G.

i=0;
do
{
j=i + 1;
while (j <n) && E

_{1}

)
j++;
if (j <n)
E

_{2}

;
}
while (i <n);
flag = 1;
for (j = 0; j <n; j++)
if ((j! = i) && E

_{3}

)
flag = 0;
if (flag)
printf(“Sink exists”);
else
printf (“Sink does not exist”);

Choose the correct expression for E

_{3}

Q. An undirected graph G with n vertices and edges is represented by adjacency list. What is the time required to generate all the connected components?

N_o/2 atoms of X(g) are converted into X⁺(g) by energy E₁. N_o/2 atoms of X(g) are converted into X^-(g) by energy E₂. Hence the ionisation potential and electron affinity of X(g) per atom are:

A. 2E₁/N_o., 2(E₂-E₁)/N_o

B. 2E₁/N_o.,. 2E₂/N_o

C. E₁-E₂/N_{o. ,.}2E₂/N_o

D. None is correct

Q. A word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as in the two matrices given below. The columns and rows of Matrix I are numbered from

0

4

and that of Matrix

I

are numbered from

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9

. A letter from these matrices can be represented first by its row and next by its column, e.g.

^{'} A^{'}

can be represented by

00, 12, 23

etc., and

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can be represented by

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		Matrix I
	$0$	$1$	$2$	$3$	$4$
$0$	$A$	$R$	$S$	$N$	$C$
$1$	$N$	$C$	$A$	$R$	$S$
$2$	$S$	$N$	$C$	$A$	$R$
$3$	$R$	$S$	$N$	$C$	$A$
$4$	$C$	$A$	$R$	$S$	$N$

		Matrix II
	$5$	$6$	$7$	$8$	$9$
$5$	$O$	$E$	$L$	$P$	$T$
$6$	$T$	$O$	$E$	$L$	$P$
$7$	$P$	$T$	$O$	$E$	$L$
$8$	$L$	$P$	$T$	$O$	$E$
$9$	$E$	$L$	$P$	$T$	$O$

Q. At time

t = 0

, a container has

N_{0}

radioactive atoms with a decay constant

λ

. In addition,

C

numbers of atoms of the same type are being added to the container per unit time. How many atoms of this type are there at

t = T

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