Degree sum calculations

Questions asking to find the sum of vertex degrees given the number of edges, or vice versa.

3 questions · Easy -1.0

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A graph has six vertices; two are of order 3 and the rest are of order 4. Calculate the number of arcs in the graph, showing your working.
Is the graph Eulerian, semi-Eulerian or neither? Give a reason to support your answer. A simple graph is one in which any two vertices are directly connected by at most one arc and no vertex is directly connected to itself. A connected graph is one in which every vertex is connected, directly or indirectly, to every other vertex.
Explain why a simple graph with six vertices, two of order 3 and the rest of order 4, must also be a connected graph.

The graph \(G\) has 2 vertices. The sum of the degrees of all the vertices of \(G\) is 6 Draw \(G\) 8
The planar graph \(P\) is Eulerian, with at least one vertex of degree \(x\), where \(x\) is a positive integer. Some of the properties of \(P\) are shown in the table below. Question number Additional page, if required. Write the question numbers in the left-hand margin. Question number Additional page, if required. Write the question numbers in the left-hand margin.