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- W2077367194 abstract "An r-labeling of the vertices of a graph $G=(V(G),E(G))$, $f:V(G)longrightarrow{1,2,ldots,r}$, is said to be distinguishing provided that no nontrivial automorphism of G preserves all of the vertex labels. The distinguishing number of G, denoted by $D(G)$, is the minimum r such that G has a distinguishing r-labeling. The distinguishing chromatic number $chi_D(G)$ of G is defined similarly, where, in addition, f is assumed to be a proper coloring. In this paper, we determine $D(G)$ and $chi_D(G)$ of the book graph $B_{m,n}$, and $chi_D(G)$ of the generalized Petersen graph $P_{n,k}$." @default.
- W2077367194 created "2016-06-24" @default.
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- W2077367194 date "2009-01-01" @default.
- W2077367194 modified "2023-09-25" @default.
- W2077367194 title "Breaking the Symmetries of the Book Graph and the Generalized Petersen Graph" @default.
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- W2077367194 doi "https://doi.org/10.1137/080728640" @default.
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