On total edge product cordial labeling of fullerenes - Martin Baca; Muhammad Irfan; Aisha Javed; Andrea Semanicova-Fenovcikova (Electronic Journal of Graph Theory and Applications (EJGTA), 2018)
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 $φ(e_1)·φ(e_2)·…· φ(e_n) \pmod k$, where e1, e2, …, en are the edges incident to the vertex v. The labeling φ is called a k-total edge product cordial labeling of G if ∣(eφ(i) + vφ * (i)) − (eφ(j) + vφ * (j))∣ ≤ 1 for every i, j, $0 \le i < j \le k-1$, where eφ(i) and vφ * (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.