Select the incorrect statement about calculating the degree of a vertex in an…
2017
Select the incorrect statement about calculating the degree of a vertex in an undirected graph:
Answer: D. Sum of all the edges in the graph — ConceptIn an undirected graph, the degree of a vertex is the number of incident edge-ends at that vertex. A non-loop edge contributes one edge-end to each…
- A.
For every regular edge on a vertex is counted as 1
- B.
For a self-loop it is counted as 2
- C.
Sum of all the edges on a vertex
- D.
Sum of all the edges in the graph
Attempted by 172 students.
Show answer & explanation
Correct answer: D
Concept
In an undirected graph, the degree of a vertex is the number of incident edge-ends at that vertex. A non-loop edge contributes one edge-end to each endpoint, while a self-loop contributes two edge-ends to its single endpoint.
Application
Focus on one vertex, not on the graph as a whole.
Count one contribution for each ordinary edge incident on that vertex.
Count two contributions for each self-loop at that vertex.
Therefore, the total number of edges in the entire graph is not a rule for finding the degree of a particular vertex.
Contrast
“Every regular edge on a vertex is counted as 1” describes the one edge-end contributed by an ordinary incident edge.
“For a self-loop it is counted as 2” describes the two edge-ends contributed at the same vertex.
“Sum of all the edges on a vertex” refers to counting the incident contributions at that vertex.
“Sum of all the edges in the graph” is a graph-wide edge count, not a vertex-specific incident-edge count.
Result
The incorrect statement is “Sum of all the edges in the graph.”