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- W2770856211 abstract "The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling with $d$ labels that is preserved only by a trivial automorphism. A list assignment to $G$ is an assignment $L = {L(v)}_{vin V (G)}$ of lists of labels to the vertices of $G$. A distinguishing $L$-labeling of $G$ is a distinguishing labeling of $G$ where the label of each vertex $v$ comes from $L(v)$. The list distinguishing number of $G$, $D_l(G)$ is the minimum $k$ such that every list assignment to $G$ in which $|L(v)| = k$ for all $v in V (G)$ yields a distinguishing $L$-labeling of $G$. In this paper, we determine the list-distinguishing number for two families of graphs. We also characterize graphs with the distinguishing number equal the list distinguishing number. Finally, we show that this characterization works for other list numbers of a graph." @default.
- W2770856211 created "2017-12-04" @default.
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- W2770856211 date "2017-11-24" @default.
- W2770856211 modified "2023-09-27" @default.
- W2770856211 title "Characterization of graphs with distinguishing number equal list distinguishing number" @default.
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