The question in my assignment is
“Draw a simple graph with $6$ vertices, and $8$ edges that contains exactly one cycle of length $4$ and two cycles of length $3$.”
I can draw a simple graph with $6$ vertices and $8$ edges but it doesn’t contain exactly one $4$-cycle and two $3$-cycles, sometimes there is one $5$-cycle in the graph as well.
Any ideas how can I construct a simple graph as the requirement said? Thank you.
From what I noticed A>B>F>E>A is a 4-cycle. A>D>E>A and B>C>F>B are 3-cycles. However, in the graph, A>B>C>F>E>A is a cycle of length 5 and A>B>C>F>E>D>A is a cycle of length 6. So, there are other cycles in the graph with cycle lengths are more than 3 and 4. Am I understanding this in the correct concept or not?