MODULAR COLORINGS OF CORONA PRODUCT OF Pm WITH Cn

N. Paramaguru

  DOI:  https://doi.org/10.37418/amsj.9.11.92

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For $\ell\ge 2,$ a modular $\ell\!$-colouring of a graph $\mathcal{G}$ except singleton nodes is a colouring of the nodes of $\mathcal{G}$ with the elements in $\mathbb{Z}_\ell$ have the possessions that for every two adjacent nodes of $\mathcal{G},$ the sums of the colours of that neighbours are different in $\mathbb{Z}_\ell.$ The lower $\ell$ for that $\mathcal{G}$ has a modular $\ell\!$-colouring is the modular chromatic number of $\mathcal{G}.$ In this paper, we discussed the modular chromatic number of corona product of paths with cycles.

Keywords: modular colorings, corona product.