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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.
##### MSC:
 05C78 Graph labelling (graceful graphs, bandwidth, etc.)
##### Keywords:
distinguishing index; distinguishing number; join
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