MATHEMATICA BOHEMICA, Vol. 124, No. 1, pp. 83-85 (1999)

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

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