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- Title
On 3-total edge product cordial labeling of grid.
- Authors
Ahmad, Ali; Hasni, Roslan; Irfan, Muhammad; Naseem, Maria; Siddiqui, Muhammad Kamran
- Abstract
Let us consider a mapping ϕ : E (G) → { 0 , 1 , ... , k − 1 } of a graph G , where k is an integer, 2 ≤ k ≤ | E (G) |. The mapping ϕ induces for every vertex v of G the label ϕ ∗ (v) = ∏ u v ∈ E (G) ϕ (u v) (mod k). Let e ϕ (i) ( v ϕ (i)) denote the number of edges (vertices) in G that are labeled with the number i under the labeling ϕ , 0 ≤ i ≤ k − 1. The function 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 0 ≤ i < j ≤ k − 1. A graph G with a k -total edge product cordial labeling is called a k -total edge product cordial graph. In this paper, we prove that the grid graph P m □ P n for m , n ≥ 2 admits a 3 -total edge product cordial labeling.
- Subjects
GRAPH labelings; EDGES (Geometry); INTEGERS
- Publication
Asian-European Journal of Mathematics, 2021, Vol 14, Issue 6, pN.PAG
- ISSN
1793-5571
- Publication type
Article
- DOI
10.1142/S1793557121500960