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On the vertex irregular reflexive labeling of generalized friendship graph and corona product of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 9، دوره 9، شماره 3، آذر 2024، صفحه 509-526 اصل مقاله (674.88 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2023.28046.1426 | ||
| نویسندگان | ||
| Kooi-Kuan Yoong1؛ Roslan Hasni* 1؛ Gee-Choon Lau2؛ Ali Ahmad3 | ||
| 1Special Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Terengganu, Malaysia | ||
| 2Universiti Teknologi MARA, Faculty of Computer and Mathematical Sciences, 85100 Segamat, Johor, Malaysia | ||
| 3College of Computer Sciences and Information Technology, Jazan University, Jazan, Saudi Arabia | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Vertex irregular reflexive labeling؛ Reflexive vertex strength؛ Generalized friendship graph؛ Corona product | ||
| مراجع | ||
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