On 3-total edge product cordial labeling of honeycomb

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.