Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 9 3 2024 09 01 On the vertex irregular reflexive labeling of generalized friendship graph and corona product of graphs 509 526 14545 10.22049/cco.2023.28046.1426 EN Kooi-Kuan Yoong Special Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Terengganu, Malaysia Roslan Hasni Special Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Terengganu, Malaysia Gee-Choon Lau Universiti Teknologi MARA, Faculty of Computer and Mathematical Sciences, 85100 Segamat, Johor, Malaysia Ali Ahmad College of Computer Sciences and Information Technology, Jazan University, Jazan, Saudi Arabia 0000-0003-3434-9908 Journal Article 2022 10 17 For a graph $G$, we define a total $k$-labeling $\varphi$ as a combination of an edge labeling $\varphi_e:E(G)\rightarrow \{1,\,2,\,\ldots,\,k_e\}$ and a vertex labeling $\varphi_v:V(G)\rightarrow \{0,\,2,\,\ldots,\,2k_v\}$, where $k=\,\mbox{max}\, \{k_e,2k_v\}$. The total $k$-labeling $\varphi$ is called a vertex irregular reflexive $k$-labeling of $G$ if any pair of vertices $u$, $u'$ have distinct vertex weights $wt_{\varphi}(u)\neq wt_{\varphi}(u')$, where $wt_{\varphi}(u)=\varphi(u)+\sum_{uu'\in E(G)} \varphi(uu')$ for any vertex $u\in V(G)$. 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. https://comb-opt.azaruniv.ac.ir/article_14545_827f4576ec34ec69917d00d963659911.pdf