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Axenovich, M.; Harant, J.; Przybyło, J.; Soták, R.; Voigt, M.; Weidelich, J.
Discrete Applied Mathematics, 05/2016, Letnik: 205Journal Article
For an assignment of numbers to the vertices of a graph, let Su be the sum of the labels of all the vertices in the closed neighborhood of u, for a vertex u. Such an assignment is called closed distinguishing if Su≠Sv for any two adjacent vertices u and v unless the closed neighborhoods of u and v coincide. In this note we investigate disG, the smallest integer k such that there is a closed distinguishing labeling of G using labels from {1,…,k}. We prove that disG≤Δ2−Δ+1, where Δ is the maximum degree of G. This result is sharp. We also consider a list-version of the function disG and give a number of related results.
