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graph operator; line graph; $k$-edge graph
A theorem is proved which implies affirmative answers to the problems of E. Prisner. One problem is whether there are cycles of the line graph operator $L$ with period other than 1, the other whether there are cycles of the 4-edge graph operator $\nabla_4$ with period greater than 2. Then a similar theorem follows.
[1] Prisner E.: Graph Dynamics. Longman House Ltd., Burnt Mill, Harlow, Essex 1995. MR 1379114 | Zbl 0848.05001
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