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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
An Identity Card has the number ABCDEFG, not necessarily in that order, where each letter represents a distinct digit (1, 2, 4, 5, 7, 8, 9 only). The number is divisible by 9. After deleting the first digit from the right, the resulting number is divisible by 6. After deleting two digits from the right of original number, the resulting number is divisible by 5. After deleting three digits from the right of original number, the resulting number is divisible by 4. After deleting four digits from the right of original number, the resulting number is divisible by 3. After deleting five digits from the right of original number, the resulting number is divisible by 2. Which of the following is a possible value for the sum of the middle three digits of the number?
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.
In a class, 24 students have scored more marks than Vineet, whereas 19 students have scored lesser marks than Surbhi. Arti has scored more marks than Surbhi, but lesser marks than Vineeet. Arti has scored lesser marks than 29 students and more marks than 26 students. How many total students are there in the class ?
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
What are the properties of a tree in a network graph? 1. It consists of all the nodes of the graph. 2. If the graph has N number of nodes, the tree will have (N – 1) branches. 3. There will be only one closed path in the tree.
A 2 digit number is reversed and added to the original number to form a new number. If the original number is multiplied by 2 and 18 is added to it, then it becomes equal to the newly formed number. The sum of digits of the original number is 16. What is the ratio of ten's digit to the unit's digit of the original number?
The number obtained by interchanging the two digits of a two-digit number is lesser than the original number by 54. If the sum of the two digit of the number is 12, then what is the original number ?
In a two-digit number, the digit at unit’s place is more than twice the digit at the tenths place by 1. If the digits at the unit place and the tenth place are interchanged, the difference between the newly formed number and the original number is less than the original number by 1. What is the original number?
There are some boys standing in a queue having weight 50 kg, 60 kg, 70 kg, 125 kg and 35 kg. The boys are A, B, C, D and E but not necessary in the same order. The one who is the heaviest has 125 kg and then 70 kg and so on. I. D is a lesser weight than E. II. B is only lesser than A and is heavier than C. III. C's only heavier than D. Whose weight is 70 kg?