Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21289320240901On the vertex irregular reflexive labeling of generalized friendship graph and corona product of graphs5095261454510.22049/cco.2023.28046.1426ENKooi-KuanYoongSpecial Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Ocean
Engineering Technology and Informatics, Universiti Malaysia Terengganu, Terengganu, MalaysiaRoslanHasniSpecial Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Ocean
Engineering Technology and Informatics, Universiti Malaysia Terengganu, Terengganu, MalaysiaGee-ChoonLauUniversiti Teknologi MARA,
Faculty of Computer
and Mathematical Sciences,
85100 Segamat,
Johor, Malaysia0000-0002-9777-6571AliAhmadCollege of Computer Sciences and Information Technology, Jazan University, Jazan, Saudi ArabiaJournal Article20221017For 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.http://comb-opt.azaruniv.ac.ir/article_14545_827f4576ec34ec69917d00d963659911.pdf