On 3-total edge product cordial labeling of honeycomb. Issue 2 (1st August 2017)

• Record Type: Journal Article
• Authors: Ahmad, Ali; Bača, Martin; Naseem, Maria; Semaničová-Feňovčíková, Andrea
• Is Part Of: AKCE International Journal of Graphs and Combinatorics. Volume 14:Issue 2(2017)
• Page Start: 149
• Page End: 157
• Publication Date: 2017-08-01
• Subjects: Cordial labeling -- k-total edge product cordial labeling -- Hexagonal grid
• DOI: 10.1016/j.akcej.2017.02.002
• Languages: English
• ISSNs: 0972-8600

Abstract

Abstract: For a graph G = ( V ( G ), E ( G ) ), an edge labeling φ : E ( G ) → { 0, 1, …, k − 1 } where k is an integer, 2 ≤ k ≤ | E ( G ) |, induces a vertex labeling φ ∗ : V ( G ) → { 0, 1, …, k − 1 } defined by φ ∗ ( v ) = φ ( e 1 ) ⋅ φ ( e 2 ) ⋅ … ⋅ φ ( e n ) ( mod k ), where e 1, e 2, …, e n are the edges incident to the vertex v . 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 every i, j, 0 ≤ i < j ≤ k − 1, where e φ ( i ) and v φ ∗ ( i ) are the number of edges e and vertices v with φ ( e ) = i and φ ∗ ( v ) = i, respectively. In this paper, we investigate the existence of 3 -total edge product cordial labeling of hexagonal grid.