Edge irregular reflexive labeling for corona product of path and star

• Published in: Palestine Journal of Mathematics
• Main Author: Yoong K.K.; Hasni R.; Lau G.C.; Gobithaasan R.U.; Siddiqui M.K.
• Format: Article
• Language: English
• Published: Palestine Polytechnic University 2024
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85186231186&partnerID=40&md5=bbb0300cf803824f81b7685916710aea

Concerning a graph G in this research, we express a total k-labeling ϕ, which represents a combination of an edge labeling given by ϕe (x) → {1, 2, …, ke } as well as a vertex labeling given by ϕv (x) → {0, 2, …, 2kv }. Here, ϕ(x) = ϕv (x) when x ∈ V (G), while ϕ(x) = ϕe (x) when x ∈ E(G), in which k = max {ke, 2kv }. Moreover, the total k-labeling ϕ is known as an edge irregular reflexive k-labeling with respect to G, provided that every edge weights differ. The edge weight represents the sum of the edge label as well as its two end-vertex labels corresponding to it. The smallest value obtained for k provided that such labelling exists refers to reflexive edge strength with respect to G. This research examines the edge irregular reflexive labelling with regard to the corona product of a path and star graph, determining its reflexive edge strength. © Palestine Polytechnic University-PPU 2024.