Geodesic
On total irregular labelings with no-hole weights of some planar graphs
Diskretnaya Matematika, Tome 36 (2024) no. 2, pp. 23-32 Cet article a éte moissonné depuis la source Math-Net.Ru

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A total edge irregular $k$-labeling of a graph $G=(V,E)$, $\partial: V\cup E \rightarrow \{1, 2, 3,\cdots,k\}$ is a labeling of vertices and edges of $G$ in such a way that the weights of all edges are distinct. A total edge irregularity strength of graph $G$, denoted by $\operatorname{tes}(G)$ is defined as the minimal $k$ for which a graph $G$ has a totally irregular total $k$-labeling. Analogously we can define total vertex irregularity strength of graph $G$, denoted by $\operatorname{tvs}(G)$. In this paper, we provide the no-hole total (both edge and vertex) irregularity strength for some well known planar graphs.
Keywords: total edge irregular $k$-labeling, total vertex irregular $k$-labeling, Triangular Snake Graph, Double Triangular Snake Graph, Quadrilateral Snake Graph. 
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     author = {S. Mitra and S. Bhoumik},
     title = {On total irregular labelings with no-hole weights of some planar graphs},
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     url = {http://geodesic.mathdoc.fr/item/DM_2024_36_2_a2/}
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S. Mitra; S. Bhoumik. On total irregular labelings with no-hole weights of some planar graphs. Diskretnaya Matematika, Tome 36 (2024) no. 2, pp. 23-32. http://geodesic.mathdoc.fr/item/DM_2024_36_2_a2/

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