TY - JOUR
ID - 14545
TI - On the vertex irregular reflexive labeling of generalized friendship graph and corona product of graphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Yoong, Kooi-Kuan
AU - Hasni, Roslan
AU - Lau, Gee-Choon
AU - Ahmad, Ali
AD - Special Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Ocean
Engineering Technology and Informatics, Universiti Malaysia Terengganu, Terengganu, Malaysia
AD - Universiti Teknologi MARA,
Faculty of Computer
and Mathematical Sciences,
85100 Segamat,
Johor, Malaysia
AD - College of Computer Sciences and Information Technology, Jazan University, Jazan, Saudi Arabia
Y1 - 2024
PY - 2024
VL - 9
IS - 3
SP - 509
EP - 526
KW - Vertex irregular reflexive labeling
KW - Reflexive vertex strength
KW - Generalized friendship graph
KW - Corona product
DO - 10.22049/cco.2023.28046.1426
N2 - 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.
UR - http://comb-opt.azaruniv.ac.ir/article_14545.html
L1 - http://comb-opt.azaruniv.ac.ir/article_14545_827f4576ec34ec69917d00d963659911.pdf
ER -