Computing the edge irregularity strengths of chain graphs and the join of two graphs

• Published in: Electronic journal of graph theory and applications Vol. 6; no. 1; p. 201
• Main Authors: Ahmad, Ali, Gupta, Ashok, Simanjuntak, Rinovia
• Format: Journal Article
• Language: English
• Published: Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia 01-01-2018
• Subjects: edge irregularity strength, blocks, chain graphs, join of graphs
• ISSN: 2338-2287; 2338-2287
• DOI: 10.5614/ejgta.2018.6.1.15

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.