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For a simple graph G  = ( V ,  E ) this paper deals with the existence of an edge labeling φ  :  E ( G ) → {0, 1, …,  k  − 1} , 2 ≤  k  ≤ ∣ E ( G )∣ , which induces a vertex labeling φ  *   :  V ( G ) → {0, 1, …,  k  − 1} in such a way that for each vertex v , assigns the label $\varphi(e_1)\cdot\varphi(e_2)\cdot\ldots\cdot \varphi(e_n) \pmod k$ , where e 1 ,  e 2 , …,  e n are the edges incident to the vertex v . The labeling φ is called a k -total edge product cordial labeling of G if ∣( e φ ( i ) +  v φ  *  ( i )) − ( e φ ( j ) +  v φ  *  ( j ))∣ ≤ 1 for every i ,  j , $0 \le i l j \le k-1$ , where e φ ( i ) and v φ  *  ( i ) is the number of edges and vertices with φ ( e ) =  i and φ  *  ( v ) =  i , respectively. The paper examines the existence of such labelings for toroidal fullerenes and for Klein-bottle fullerenes.

On total edge product cordial labeling of fullerenes