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Ars Combinatoria

  • Research article

The Connected Domination and Tree Domination of \(P(n,k)\) for \(k = 1,2, \lfloor n/2 \rfloor\)

Zhao Chengye1,2, Yang Yuansheng2, Sun Linlin2, Cao Feilong1
1College of Science, China Jiliang University Hangzhou , 310018, P. R. China
2Department of Computer Science, Dalian University of Technology Dalian, 116024, P. R. China
  • Published: 31/07/2011

Abstract

Let \(\gamma_c(G)\) be the connected domination number of \(G\) and \(\gamma_{tr}(G)\) be the tree domination number of \(G\). In this paper, we study the generalized Petersen graphs \(P(n,k)\), prove \(\gamma_c(P(n, k)) = \gamma_{tr}(P(n, k))\) and show their exact values for \(k = 1, 2, \ldots, \lfloor n/2 \rfloor\).

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Citation
Zhao Chengye, Yang Yuansheng, Sun Linlin, Cao Feilong. The Connected Domination and Tree Domination of \(P(n,k)\) for \(k = 1,2, \lfloor n/2 \rfloor\)[J], Ars Combinatoria, Volume 101. 467-479. .