*We study the Homfly polynomial of periodic knotted trivalent plane graphs introduced in [1]. We show how periodicity of a knotted trivalent plane graphs is reflected in this polynomial. In particular, we derive congruences of periodic knotted trivalent plane graphs in terms of this polynomial invariant. These congruences yield criteria for periodicity of knotted trivalent plane graphs.*

Author(s) Details

**Ayman A. Aboufattoum***Department of Mathematics, Faculty of Science, Kuwait University, P.O.Box 5969, Safat-13060, Kuwait.*

**K. Qazaqzeh***Department of Mathematics, Faculty of Science, Kuwait University, P.O.Box 5969, Safat-13060,Kuwait.*

**E. A. Elsakhawy***Department of Mathematics, Faculty of Science, Ain Shams University, Cairo 11566, Egypt.*

**A. T. Diab***Department of Mathematics, Faculty of Science, Ain Shams University, Cairo 11566, Egypt.*

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