Abstract
A subset \(S \subseteq V(G)\) in a graph \(G=(V,E)\) is a connected [j, k]-set, if it satisfies that G[S] is a connected subgraph of G and every vertex \(v \in V \setminus S\), \(j \le |N(v) \cap S| \le k\) for non-negative integers \(j<k\). In this paper, we study the connected [1, 2]-domination number of graph G, which denoted \(\gamma _{c[1,2]}(G)\). We discussed the graphs with \(\gamma _{c[1,2]}(G)=n\) and the graphs with \(\gamma _{c[1,2]}(G)=\gamma _c(G)\). In the end, the CONNECTED [1, 2]-SET Problem has been proved to be NP-complete for bipartite graphs.
Supported by Natural science fundation of Zhejiang province (No. LY14F020040), Natural Science Foundation of China (No. 61173002)and Natural Science Foundation of Jiangsu University (No. 16KJB110011).
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Zhang, C., Zhao, C. (2018). Connected [1,2]-Sets in Graphs. In: Li, L., Lu, P., He, K. (eds) Theoretical Computer Science. NCTCS 2018. Communications in Computer and Information Science, vol 882. Springer, Singapore. https://doi.org/10.1007/978-981-13-2712-4_7
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DOI: https://doi.org/10.1007/978-981-13-2712-4_7
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