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If for some positive integer k, degree of vertex d(v)=k for every vertex v of the graph G, then G is called ______.
- a)K graph
- b)K-regular graph
- c)Empty graph
- d)All of above
Correct answer is option 'B'. Can you explain this answer?
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If for some positive integer k, degree of vertex d(v)=k for every vert...
A graph in which all vertices are of equal degree is called regular graph.
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If for some positive integer k, degree of vertex d(v)=k for every vert...
Answer:
A graph is a mathematical representation of a set of objects, called vertices, along with a set of connections between these objects, called edges. In this context, a vertex represents a point or a node, and an edge represents a connection or a relationship between two vertices.
A graph G is said to be k-regular if the degree of each vertex in G is equal to k. The degree of a vertex is defined as the number of edges incident to that vertex. So, if for every vertex v in G, the degree of v is k, then G is called a k-regular graph.
Let's analyze the given options:
a) K graph: The term "K graph" is not a standard term in graph theory. It is unclear what it refers to, so it cannot be the correct answer.
b) K-regular graph: As mentioned earlier, a graph G is called a k-regular graph if the degree of every vertex in G is equal to k. This is exactly the condition given in the question. Therefore, the correct answer is option B.
c) Empty graph: An empty graph is a graph with no vertices and no edges. Since the given graph G has vertices (as mentioned in the question), it cannot be an empty graph. Hence, option C is incorrect.
d) All of above: This option includes all the previous options (a, b, and c). Since option C is incorrect (as explained above), option D cannot be the correct answer.
In conclusion, the correct answer is option B, which states that if the degree of every vertex v in the graph G is equal to k, then G is called a k-regular graph.
A graph is a mathematical representation of a set of objects, called vertices, along with a set of connections between these objects, called edges. In this context, a vertex represents a point or a node, and an edge represents a connection or a relationship between two vertices.
A graph G is said to be k-regular if the degree of each vertex in G is equal to k. The degree of a vertex is defined as the number of edges incident to that vertex. So, if for every vertex v in G, the degree of v is k, then G is called a k-regular graph.
Let's analyze the given options:
a) K graph: The term "K graph" is not a standard term in graph theory. It is unclear what it refers to, so it cannot be the correct answer.
b) K-regular graph: As mentioned earlier, a graph G is called a k-regular graph if the degree of every vertex in G is equal to k. This is exactly the condition given in the question. Therefore, the correct answer is option B.
c) Empty graph: An empty graph is a graph with no vertices and no edges. Since the given graph G has vertices (as mentioned in the question), it cannot be an empty graph. Hence, option C is incorrect.
d) All of above: This option includes all the previous options (a, b, and c). Since option C is incorrect (as explained above), option D cannot be the correct answer.
In conclusion, the correct answer is option B, which states that if the degree of every vertex v in the graph G is equal to k, then G is called a k-regular graph.
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If for some positive integer k, degree of vertex d(v)=k for every vertex v of the graph G, then G is called ______.a)K graphb)K-regular graphc)Empty graphd)All of aboveCorrect answer is option 'B'. Can you explain this answer?
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