The b-chromatic number of powers of hypercube

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• 作者：P. Francis ^{selvafrancis@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; S. Francis Raj ^{francisraj_s@yahoo.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：b-coloring ; b-chromatic number ; hypercubes ; power of a graph
• 刊名：Electronic Notes in Discrete Mathematics
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：53
• 期：Complete
• 页码：459-464
• 全文大小：190 K

文摘

A b-coloring of a graph G with k colors is a proper coloring of G using k colors in which each color class contains a vertex which has a neighbor in each of the other color classes. The largest positive integer k for which G has a b-coloring using k   colors is the b-chromatic number b(G)$b(G)$ of G  . In this paper, we obtain bounds for the b-chromatic number of powers of Q_n$Q_n$, namely $Q_n^p$ for all n≥5$n\ge 5$ and $\lfloor \frac{n}{2}\rfloor <p<n-1$. Also we obtain exact value of the b-chromatic number of Q^p−n$Q^p-n$ for all n≥3$n\ge 3$, and $p=\lfloor \frac{n}{2}\rfloor$ and 523017a4929670ff678d2448c9e6" title="Click to view the MathML source">p=n−1$p=n-1$.