Must a graph with 68 nodes and 72 edges have a circuit Expla

Must a graph with 68 nodes and 72 edges have a circuit? Explain your reasoning and justify your answer

Solution

A circuit can be a closed walk allowing repetitions of vertices but not edges.

starting vertex and ending vertex should be same.

in this case we have 68 nodes(vertex ) and 72 edges

it is not necessary that graph with 68 nodes and 72 edges must form a circuit

beacause,

To form circuit, edges at each node of graph must be in pairs

i.e degree of each vertex should be even.

which is not true in every possible case