Computing the edge irregularity strengths of chain graphs and the join of two graphs
| Main Authors: | Ahmad, Ali; College of Computer Science & Information Systems, Jazan University, Jazan, Saudi Arabia, Gupta, Ashok; College of Computer Science & Information Systems, Jazan University, Jazan, Saudi Arabia, Simanjuntak, Rinovia; Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesa 10 Bandung 40132, Indonesia. |
|---|---|
| Other Authors: | We thank the Deanship of Research, Jazan University for supporting this project under the Grant No. 000114/7/37. |
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2018
|
| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/474 https://www.ejgta.org/index.php/ejgta/article/view/474/pdf_75 |
Daftar Isi:
- In computer science, graphs are used in variety of applications directly or indirectly. Especially quantitative labeled graphs have played a vital role in computational linguistics, decision making software tools, coding theory and path determination in networks. For a graph G(V, E) with the vertex set V and the edge set E, a vertex k-labeling φ : V → {1, 2, ..., k} is defined to be an edge irregular k-labeling of the graph G if for every two different edges e and f their wφ(e) ≠ wφ(f), where the weight of an edge e = xy ∈ E(G) is wφ(xy) = φ(x) + φ(y). The minimum k for which the graph G has an edge irregular k-labeling is called the edge irregularity strength of G, denoted by es(G). In this paper, we determine the edge irregularity strengths of some chain graphs and the join of two graphs. We introduce a conjecture and open problems for researchers for further research.