On 3-total edge product cordial labeling of a carbon nanotube network. Issue 3 (1st December 2019)

• Record Type: Journal Article
• Authors: Bača, Martin; Irfan, Muhammad; Semaničová-Feňovčíková, Andrea
• Is Part Of: AKCE International Journal of Graphs and Combinatorics. Volume 16:Issue 3(2019)
• Page Start: 310
• Page End: 318
• Publication Date: 2019-12-01
• Subjects: Cordial labeling -- k-total edge product cordial labeling -- Carbon nanotube network
• DOI: 10.1016/j.akcej.2018.09.001
• Languages: English
• ISSNs: 0972-8600

Abstract

Abstract: For a simple graph G = ( V, E ) with the vertex set V and the edge set E and for an integer k, 2 ≤ k ≤ | E ( G ) |, an edge labeling φ : E ( G ) → { 0, 1, …, k − 1 } 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 and vertices with φ ( e ) = i and φ ∗ ( v ) = i, respectively. In this paper, we investigate the 3-total edge product cordial labeling of a carbon nanotube network.