Abstract
Let \(G = (V, E)\) be an arbitrary graph. For any subset X of V, let B(X) be the set of all vertices in \(V-X\) that have a neighbour in X. Mashburn et al. defined the differential of a set X to be \(\partial (X) = |B(X)| - |X|\), and the differential of a graph is max\(\{\partial (X)\}\), where the maximum is taken over all subsets X of V. Motivated by this parameter we define the restrained differential of graph as follows. For any subset X of V, let \(\overline{B}(X)\) be the set of all vertices in \(V-X\) that have a neighbor in X and a neighbour in \(V-X\). We define the restrained differential of a set X to be \(\overline{\partial }(X) = |\overline{B}(X)| - |X|\) and the restrained differential of a graph is max\(\{\overline{\partial }(X)\}\), where the maximum is taken over all subsets X of V. In this paper, we initiate a study of this parameter.
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Pushpam, P.R.L., Yokesh, D. (2017). Restrained Differential of a Graph. In: Arumugam, S., Bagga, J., Beineke, L., Panda, B. (eds) Theoretical Computer Science and Discrete Mathematics. ICTCSDM 2016. Lecture Notes in Computer Science(), vol 10398. Springer, Cham. https://doi.org/10.1007/978-3-319-64419-6_43
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DOI: https://doi.org/10.1007/978-3-319-64419-6_43
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