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Keywords:
graph operator; line graph; \$k\$-edge graph
Summary:
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.
References:
[1] Prisner E.: Graph Dynamics. Longman House Ltd., Burnt Mill, Harlow, Essex 1995. MR 1379114 | Zbl 0848.05001

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