D1 graphs query

I would post this as anonymous seeing as how everyone seems to think D1 is a breeze... but i'm stuck on this quetsion.

The cycles i've got are
ABCA, ABCDA, ABCDEA, ABCEA
ACDA ACEA ACDEA
ADEA

They're mostly right apart from the ones in red which aren't in the answers. I was wondering if the book missed these diagonal ones out ? I can't think of how they could be wrong because the definition of a cycle says nothing about whether or not they're allowed to cross other edges.

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Reply 1

Kyalimers

I'm quite perplexed as well.

Reply 2

wellison999

Those are definitely fine as cycles - the one's in red are subgraphs isomorphic to

C_3

C_4

hence satisfy the definition. Crossing over of edges is fine and is allowed in graph theory (how else would you draw e.g. a cube where each corner is a vertex?) - a picture is just a representation of the graph after all.