Local Distance Antimagic Vertex Coloring of Graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866913622113910784 |
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| author | T, Divya S, Devi Yamini |
| author_facet | T, Divya S, Devi Yamini |
| contents | A bijective function $f:V\rightarrow\left\{1,2,3,...,|V| \right\}$ is said to be a local distance antimagic labeling of a graph $G=(V,E)$, if $w(u)\neq w(v)$ for any two adjacent vertices $u, v$ where the weight $w(v)=\sum_{z\in N(v)}f(z)$. The local distance antimagic labeling of $G$ induces a proper coloring in $G$, called local distance antimagic chromatic number denoted by $χ_{ld}(G)$. In this article, we introduce the parameter $χ_{ld}(G)$ and compute the local distance antimagic chromatic number of graphs.
Keywords: Distance antimagic labeling, Local distance antimagic labeling, Local distance antimagic chromatic number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_01833 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Local Distance Antimagic Vertex Coloring of Graphs T, Divya S, Devi Yamini Combinatorics A bijective function $f:V\rightarrow\left\{1,2,3,...,|V| \right\}$ is said to be a local distance antimagic labeling of a graph $G=(V,E)$, if $w(u)\neq w(v)$ for any two adjacent vertices $u, v$ where the weight $w(v)=\sum_{z\in N(v)}f(z)$. The local distance antimagic labeling of $G$ induces a proper coloring in $G$, called local distance antimagic chromatic number denoted by $χ_{ld}(G)$. In this article, we introduce the parameter $χ_{ld}(G)$ and compute the local distance antimagic chromatic number of graphs. Keywords: Distance antimagic labeling, Local distance antimagic labeling, Local distance antimagic chromatic number. |
| title | Local Distance Antimagic Vertex Coloring of Graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2106.01833 |