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The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?
I. 7, 6, 5, 4, 4, 3, 2, 1
II. 6, 6, 6, 6, 3, 3, 2, 2
III. 7, 6, 6, 4, 4, 3, 2, 2
IV. 8, 7, 7, 6, 4, 2, 1, 1
II. 6, 6, 6, 6, 3, 3, 2, 2
III. 7, 6, 6, 4, 4, 3, 2, 2
IV. 8, 7, 7, 6, 4, 2, 1, 1
- a)I and II
- b)III and IV
- c)IV only
- d)II and IV
Correct answer is option 'D'. Can you explain this answer?
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The degree sequence of a simple graph is the sequence of the degrees o...
A generic algorithm or method to solve this question is 1: procedure isV alidDegreeSequence(L) 2: for n in list L do 3: if L doesn’t have n elements next to the current one then return false 4: decrement next n elements of the list by 1 5: arrange it back as a degree sequence, i.e. in descending order 6: if any element of the list becomes negative then return false 7: return true Rationale behind this method comes from the properties of simple graph. Enumerating the f alse returns, 1) if L doesn’t have enough elements after the current one or 2) if any element of the list becomes negative, then it means that there aren’t enough nodes to accommodate edges in a simple graph fashion, which will lead to violation of either of the two conditions of the simple graph (no self-loops and no multiple-edges between two nodes), if not others.
: → According to this theorem, Let D be sequence the d1,d2,d2. . . dn with d1 ≥ d2 ≥ d2 ≥ . . . dn for n≥ 2 and di ≥ 0. → Then D0 be the sequence obtained by: → Discarding d1, and → Subtracting 1 from each of the next d1 entries of D. → That is Degree sequence D0 would be : d2-1, d2-1, d3-1 . . . , dd1+1 -1 . . . , dn → Then, D is graphical if and only if D0 is graphical. Now, we apply this theorem to given sequences: option I) 7,6,5,4,4,3,2,1 → 5,4,3,3,2,1,0 → 3,2,2,1,0,0 → 1,1,0,0,0 → 0,0,0,0 so its graphical. Option II) 6,6,6,6,3,3,2,2 → 5,5,5,2,2,1,2 ( arrange in ascending order) → 5,5,5,2,2,2,1 → 4,4,1,1,1,0 → 3,0,0,0,0 → 2,-1,-1,-1,0 but d (degree of a vertex) is non negative so its not a graphical. Option III) 7,6,6,4,4,3,2,2 → 5,5,3,3,2,1,1 → 4,2,2,1,1,0 → 1,1,0,0,0 → 0,0,0,0 so its graphical. Option IV) 8,7,7,6,4,2,1,1 , here degree of a vertex is 8 and total number of vertices are 8 , so it’s impossible, hence it’s not graphical. Hence only option I) and III) are graphic sequence and answer is option-D
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The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?I. 7, 6, 5, 4, 4, 3, 2, 1II. 6, 6, 6, 6, 3, 3, 2, 2III. 7, 6, 6, 4, 4, 3, 2, 2IV. 8, 7, 7, 6, 4, 2, 1, 1a)I and IIb)III and IVc)IV onlyd)II and IVCorrect answer is option 'D'. Can you explain this answer?
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The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?I. 7, 6, 5, 4, 4, 3, 2, 1II. 6, 6, 6, 6, 3, 3, 2, 2III. 7, 6, 6, 4, 4, 3, 2, 2IV. 8, 7, 7, 6, 4, 2, 1, 1a)I and IIb)III and IVc)IV onlyd)II and IVCorrect answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?I. 7, 6, 5, 4, 4, 3, 2, 1II. 6, 6, 6, 6, 3, 3, 2, 2III. 7, 6, 6, 4, 4, 3, 2, 2IV. 8, 7, 7, 6, 4, 2, 1, 1a)I and IIb)III and IVc)IV onlyd)II and IVCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?I. 7, 6, 5, 4, 4, 3, 2, 1II. 6, 6, 6, 6, 3, 3, 2, 2III. 7, 6, 6, 4, 4, 3, 2, 2IV. 8, 7, 7, 6, 4, 2, 1, 1a)I and IIb)III and IVc)IV onlyd)II and IVCorrect answer is option 'D'. Can you explain this answer?.
The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?I. 7, 6, 5, 4, 4, 3, 2, 1II. 6, 6, 6, 6, 3, 3, 2, 2III. 7, 6, 6, 4, 4, 3, 2, 2IV. 8, 7, 7, 6, 4, 2, 1, 1a)I and IIb)III and IVc)IV onlyd)II and IVCorrect answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?I. 7, 6, 5, 4, 4, 3, 2, 1II. 6, 6, 6, 6, 3, 3, 2, 2III. 7, 6, 6, 4, 4, 3, 2, 2IV. 8, 7, 7, 6, 4, 2, 1, 1a)I and IIb)III and IVc)IV onlyd)II and IVCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?I. 7, 6, 5, 4, 4, 3, 2, 1II. 6, 6, 6, 6, 3, 3, 2, 2III. 7, 6, 6, 4, 4, 3, 2, 2IV. 8, 7, 7, 6, 4, 2, 1, 1a)I and IIb)III and IVc)IV onlyd)II and IVCorrect answer is option 'D'. Can you explain this answer?.
Solutions for The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?I. 7, 6, 5, 4, 4, 3, 2, 1II. 6, 6, 6, 6, 3, 3, 2, 2III. 7, 6, 6, 4, 4, 3, 2, 2IV. 8, 7, 7, 6, 4, 2, 1, 1a)I and IIb)III and IVc)IV onlyd)II and IVCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
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Here you can find the meaning of The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?I. 7, 6, 5, 4, 4, 3, 2, 1II. 6, 6, 6, 6, 3, 3, 2, 2III. 7, 6, 6, 4, 4, 3, 2, 2IV. 8, 7, 7, 6, 4, 2, 1, 1a)I and IIb)III and IVc)IV onlyd)II and IVCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?I. 7, 6, 5, 4, 4, 3, 2, 1II. 6, 6, 6, 6, 3, 3, 2, 2III. 7, 6, 6, 4, 4, 3, 2, 2IV. 8, 7, 7, 6, 4, 2, 1, 1a)I and IIb)III and IVc)IV onlyd)II and IVCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?I. 7, 6, 5, 4, 4, 3, 2, 1II. 6, 6, 6, 6, 3, 3, 2, 2III. 7, 6, 6, 4, 4, 3, 2, 2IV. 8, 7, 7, 6, 4, 2, 1, 1a)I and IIb)III and IVc)IV onlyd)II and IVCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?I. 7, 6, 5, 4, 4, 3, 2, 1II. 6, 6, 6, 6, 3, 3, 2, 2III. 7, 6, 6, 4, 4, 3, 2, 2IV. 8, 7, 7, 6, 4, 2, 1, 1a)I and IIb)III and IVc)IV onlyd)II and IVCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?I. 7, 6, 5, 4, 4, 3, 2, 1II. 6, 6, 6, 6, 3, 3, 2, 2III. 7, 6, 6, 4, 4, 3, 2, 2IV. 8, 7, 7, 6, 4, 2, 1, 1a)I and IIb)III and IVc)IV onlyd)II and IVCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
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