Bissoy.com
Doctors Medicines MCQs Q&A

Let G be a simple undirected graph. Let TD be a depth first search tree of G. Let TB be a breadth first search tree of G. Consider the following statements. (I) No edge of G is a cross edge with respect to TD. (A cross edge in G is between two nodes neither of which is an ancestor of the other in TD .) (II) For every edge (u, v) of if u is at depth i and v is at depth j in TB , then |? − ?| = 1. Which of the statements above must necessarily be true?

Let G be a simple undirected graph. Let TD be a depth first search tree of G. Let TB be a breadth first search tree of G. Consider the following statements. (I) No edge of G is a cross edge with respect to TD. (A cross edge in G is between two nodes neither of which is an ancestor of the other in TD .) (II) For every edge (u, v) of if u is at depth i and v is at depth j in TB , then |? − ?| = 1. Which of the statements above must necessarily be true? Correct Answer I only

Undirected graph cant have cross edges in DFS forest. Hence statement 1 is TRUE.

Using triangle graph we can counter the second statement.

Related Questions

Which of the following statements regarding tree are correct? (A) All the links of a tree together does not constitute the complement of the corresponding tree (B) A connected subgraph of a connected graph is a tree if there exist (n - 1) nodes of the group (C) A connected subgraph of a connected graph is a tree if there exist many paths between any pair of nodes in it (D) The number of terminal nodes of end vertices of every tree are atleast two (E) Every connected graph has atleast one tree Choose the correct answer from the options given below: (1) (A) and (B) only (2) (B) and (C) only (3) (B) and (D) only (4) (D) and (E) only
The line graph L(G) of a simple graph G is defined as follows: There is exactly one vertex v(e) in L(G) for each edge e in G. For any two edges e and e' in G, L(G) has an edge between v(e) and v(e'), if and only if e and e' are incident with the same vertex in G. Which of the following statements is/are TRUE? (P) The line graph of a cycle is a cycle. (Q) The line graph of a clique is a clique. (R) The line graph of a planar graph is planar. (S) The line graph of a tree is a tree.
The following are the conditions for selecting list of a suitable candidates to be called for interview after the written test for the recruitment is conducted/organized for management - level persons for a multi - national company. For providing accounting services and sales the candidate must (a) be holding a graduation in basic science with 65% or above or B.E. degree with 55% and above marks (b) have passed the written test with 70% or above marks (c) the age must be in the group 25 to 30 years as on 1/4/18 (d) have experience in an accounting firms for three years and diploma in accounting with 60% or above marks (e)  be presently drawing CTC of 6 Lakhs per annum and above In case the applicant who satisfies all other terms above except 1) at (a) above, then be referred as Junior Accountant 2) at (d) & (e) above then be referred as Trainee - Accountant Satisfying all the above with experience of 5 years then the referred as senior-Accountant Satisfying all the above criteria (a - e) with CA/ICWA/MBA (Finance) then be referred as manager (Accounts) Read all the above information and answer the following question Praveen has done his Masters in physics. He has no experience in accounting neither diploma. He is ready to be on training for accounting after joining. For which position he may be referred
The following are the conditions for selecting a list of suitable candidates to be called for interview after the written test for the recruitment is conducted/ organized for management-level persons for a multi-national company. For providing accounting services and sales the candidate must (a) beholding graduation in basic science with 65% or above or B.E. degree with 55% and above marks (b) have passed the written test with 70% or above marks (c) the age must be in the group 25 to 30 years as on 1/4/18 (d) have experience in an accounting firm for three years and a diploma in accounting with 60% or above marks e) be presently drawing CTC 6 lakhs per annum and above In case the applicant who satisfies all other terms above except 1) at (a) above, then be referred to as Junior Accountant 2) at (d) & (e) above then be referred to as Trainee-Accountant Satisfying all the above with experience of 5 years then be referred to as senior-Accountant Satisfying all the above criteria (a-e) with CA/ICWA/MBA (Finance) then be referred to as manager (Accounts) Read all the above information and answer the following question   Praveen has done his Masters in physics. He has no experience in accounting neither diploma. He is ready to be on training for accounting after joining. For which position he may be referred.
Read the following statements and answer with the help of given below:
(1) Two persons are said to be related to each other by full blood when they are descended from a common ancestor by the same wife.
(2) Two persons are said to be related to each other by uterine blood when they are descended from a common ancestress but by different husbands.
(3) Two persons are said to be related to each other by half blood when they are descended from a common ancestor by the same wife.
(4) Two persons are said to be related to each other by half blood when they are descended from a common ancestor but by different wives.
Let G be a connected undirected weighted graph. Consider the following two statements. S1: There exists a minimum weight edge in G which is present in every minimum spanning tree of G. S2: If every edge in G has distinct weight, then G has a unique minimum spanning tree. Which one of the following options is correct?
G = (V, E) is an undirected simple graph in which each edge has a distinct weight, and e is a particular edge of G. Which of the following statements about the minimum spanning trees (MSTs) of G is/are TRUE? I. If e is the lightest edge of some cycle in G, then every MST of G includes e II. If e is the heaviest edge of some cycle in G, then every MST of G excludes e 
Let G = (V, E) be any connected undirected edge-weighted graph. The weights of the edges in E are positive and distinct. Consider the following statements: I) Minimum Spanning Tree of G is always unique. II) Shortest path between any two vertices of G is always unique. Which of the above statements is/are necessarily true?
Directions: Seven different boxes A, B, C, D, E, F and G of different colours viz., Orange, Pink, Purple, Yellow, Blue, Red and Green are arranged one above the other. The box at the bottom of arrangement is numbered 1, the above box is numbered 2 and so on. B is immediately above E. More than two boxes are above the Orange box. The Yellow box is immediately below A. Only one box is between the Orange box and F. G is immediately above the Red box. Only one box is between B and the Pink box. Only two boxes are between the Pink and the Green box. Only two boxes are between the Yellow box and the Orange box. The Purple box is neither at the top nor at the bottom of the arrangement.B is above Pink box. C is immediately above F. Neither C nor G is a Yellow box. G is not a Orange box. Question: Which combination represents the position of C and its colour?
Consider a weight balanced tree such that, the number of nodes in the left sub tree is at least half and at most twice the number of nodes in the right sub tree. The maximum possible height (number of nodes on the path from the root to the farthest leaf) of such a tree on k nodes can be described as