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The locating chromatic number of a graph is the smallest integer $n$ such that there is a proper $n$-coloring $c$ and every vertex has a unique vector of distances to colors in $c$. We explore the necessary conditions and provide sufficient condition
Externí odkaz:
http://arxiv.org/abs/2104.04914
The locating-chromatic number of a graph $G$ is the smallest integer $n$, such that $G$ has a proper $n$-coloring $c$ and all vertices have different vectors of distances to the colors generated by $c$. We study the asymptotic value of the locating-c
Externí odkaz:
http://arxiv.org/abs/2001.00312
Autor:
Hafidh, Yusuf, Baskoro, Edy Tri
Chen et al. (2004) strongly conjectured that R(Tn,Wm)=2n-1 if the maximum degree of Tn is small and m is even. Related to the conjecture, it is interesting to know for which tree Tn, we have R(Tn,Wm) > 2n-1 for even m. In this paper, we find the Rams
Externí odkaz:
http://arxiv.org/abs/1912.05772
Autor:
Hafidh, Yusuf, Baskoro, Edy Tri
Some coloring algorithms gives an upper bound for the locating chromatic number of trees with all the vertices not in an end-path colored by only two colors. That means, a better coloring algorithm could be achieved by optimizing the number of colors
Externí odkaz:
http://arxiv.org/abs/1912.05775
Autor:
Hafidh, Yusuf, Kurniawan, Rizki, Saputro, Suhadi, Simanjuntak, Rinovia, Tanujaya, Steven, Uttunggadewa, Saladin
Let $G$ be a connected graph and $W$ be a set of vertices of $G$. The representation multiset of a vertex $v$ with respect to $W$, $r_m (v|W)$, is defined as a multiset of distances between $v$ and the vertices in $W$. If $r_m (u |W) \neq r_m(v|W)$ f
Externí odkaz:
http://arxiv.org/abs/1908.05879
Akademický článek
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Autor:
Hafidh, Yusuf1 yusufhafidh@math.itb.ac.id, Baskoro, Edy Tri1 ebaskoro@math.itb.ac.id
Publikováno v:
International Journal of Mathematics & Computer Science. 2022, Vol. 17 Issue 1, p377-394. 18p.
Autor:
Hafidh, Yusuf1 (AUTHOR), Baskoro, Edy Tri1 (AUTHOR) ebaskoro@math.itb.ac.id
Publikováno v:
Bulletin of the Malaysian Mathematical Sciences Society. Jul2021, Vol. 44 Issue 4, p2151-2160. 10p.
We study the asymptotic value of the locating chromatic number of a $k$-level $n$-ary tree. The locating chromatic number of this tree act very differently when $k$ goes to infinity and when $n$ goes to infinity. If we fix $k\geq2$, almost all $n$-ar
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3addd168c0a0e0c219fc627bea8bc423
http://arxiv.org/abs/2001.00312
http://arxiv.org/abs/2001.00312