Geodesic
Set vertex colorings and joins of graphs
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 929-941

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

For a nontrivial connected graph $G$, let $c\: V(G)\to \Bbb N$ be a vertex coloring of $G$ where adjacent vertices may be colored the same. For a vertex $v$ of $G$, the neighborhood color set ${\rm NC}(v)$ is the set of colors of the neighbors of $v$. The coloring $c$ is called a set coloring if ${\rm NC}(u)\ne {\rm NC}(v)$ for every pair $u,v$ of adjacent vertices of $G$. The minimum number of colors required of such a coloring is called the set chromatic number $\chi _s(G)$. A study is made of the set chromatic number of the join $G + H$ of two graphs $G$ and $H$. Sharp lower and upper bounds are established for $\chi _s(G+H)$ in terms of $\chi _s(G)$, $\chi _s(H)$, and the clique numbers $\omega (G)$ and $\omega (H)$.
Classification : 05C15
Keywords: neighbor-distinguishing coloring; set coloring; neighborhood color set 
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     title = {Set vertex colorings and joins of graphs},
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Okamoto, Futaba; Rasmussen, Craig W.; Zhang, Ping. Set vertex colorings and joins of graphs. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 929-941. http://geodesic.mathdoc.fr/item/CMJ_2009__59_4_a4/