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Distinguishing number and distinguishing index of join of two specific graphs. (English) Zbl 1358.05241
Summary: The distinguishing number (index) \(D(G)\) (\(D^\prime(G)\)) of a graph \(G\) is the least integer \(d\) such that \(G\) has a vertex labeling (edge labeling) with \(d\) labels that is preserved only by a trivial automorphism. In this paper, we compute the distinguishing number and the distinguishing index for the join of two specific graphs.
05C78 Graph labelling (graceful graphs, bandwidth, etc.)
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