TOC Finite automata

Question

If n state finite automata accespts infinite language then what is the length of min, and max. cycle?

Comments

Can we call self-loop a cycle?

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all cycles are loops and loop is self and non self also.

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min - 1

max - no limit since this is infinite language

Answer 1

if there is no self loop.

then min.-N   and max.-2N-1

Comments

Can you please provide some valid reason for this answer to understand?

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Your answer is right as i got some theorem related to this.Request you to please explain.
I have added theorem here:-https://gateoverflow.in/104257/toc-finite-automata-infinite-language

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you should go through pumping lemma theorem.

take any example- N=4

try all possibility of loops except self loop THEN you 'll get it.

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I tried on this,please confirm

Say I have four states a,b,c,d in my machine now after traversing from a to d ,the string went back to some state(start state),means as of now it is not accespted,now when it again come to d,we came to know that some loop has been pumped.Is it correct understanding?

But then when i went from a->d and then came to a,isnt it sufficient to say that we have a loop,?Why do we want to enter final state again.Please explain once .I have gone through pumping lemma theorem ,but this is best i could think as of now:(