A note on edge irregularity strength of Dandelion graph
| Autor: | Nagesh, H. M. |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For a simple graph $G$, a vertex labeling $\phi:V(G) \rightarrow \{1, 2,\ldots,k\}$ is called $k$-labeling. The weight of an edge $xy$ in $G$, written $w_{\phi}(xy)$, is the sum of the labels of end vertices $x$ and $y$, i.e., $w_{\phi}(xy)=\phi(x)+\phi(y)$. A vertex $k$-labeling is defined to be an edge irregular $k$-labeling of the graph $G$ if for every two different edges $e$ and $f$, $w_{\phi}(e) \neq w_{\phi}(f)$. The minimum $k$ for which the graph $G$ has an edge irregular $k$-labeling is called the edge irregularity strength of $G$, written $es(G)$. In this note, we find the exact value of edge irregularity strength of Dandelion graph when $\Delta(G) \geq \lceil \frac{|E(G)|+1}{2} \rceil$; and determine the bounds when $\Delta(G) < \lceil \frac{|E(G)|+1}{2} \rceil $. Comment: To appear in the Southeast Asian Bulletin of Mathematics |
| Databáze: | arXiv |
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