On total edge product cordial labeling of fullerenes - Martin Baca; Muhammad Irfan; Aisha Javed; Andrea Semanicova-Fenovcikova (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 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) 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 i < j 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.