On the vertex irregular reflexive labeling of generalized friendship graph and corona product of graphs

• Published in: Communications in Combinatorics and Optimization
• Main Author: Yoong K.K.; Hasni R.; Lau G.C.; Ahmad A.
• Format: Article
• Language: English
• Published: Azarbaijan Shahid Madani University 2024
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85194837207&doi=10.22049%2fCCO.2023.28046.1426&partnerID=40&md5=8f80e728c37fe39409056b1f7e9a3c3e

For a graph G, we define a total k-labeling φ as a combination of an edge labeling φe : E(G) → {1, 2, . . ., ke} and a vertex labeling φv : V (G) → {0, 2, . . ., 2kv}, where k = max {ke, 2kv}. The total k-labeling φ is called a vertex irregular reflexive k-labeling of G if any pair of vertices u, u' have distinct vertex weights wtφ(u) 6≠ wtφ(u'), where wtφ(u) = φ(u) + Puu'∈E(G) φ(uu') for any vertex u ∈ V (G). The smallest value of k for which such a labeling exists is called the reflexive vertex strength of G, denoted by rvs(G). In this paper, we present a new lower bound for the reflexive vertex strength of any graph. We investigate the exact values of the reflexive vertex strength of generalized friendship graphs, corona product of two paths, and corona product of a cycle with isolated vertices by referring to the lower bound. This study discovers some interesting open problems that are worth further exploration. © 2024 Azarbaijan Shahid Madani University.