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MATHEMATICA BOHEMICA, Vol. 124, No. 1, pp. 83-85 (1999)
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# A remark on graph operators

## Bohdan Zelinka

* Bohdan Zelinka*, Katedra aplikované matematiky Technické univerzity, Voronezska 13, 461 17 Liberec 1, Czech Republic

**Abstract:**
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.

**Keywords:** graph operator, line graph, $k$-edge graph

**Classification (MSC2000):** 05C99

**Full text of the article:**

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