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Graphs and Combinatorics

, Volume 29, Issue 4, pp 843–856 | Cite as

Upper Bounds on the Paired Domination Subdivision Number of a Graph

  • Yoshimi Egawa
  • Michitaka Furuya
  • Masanori Takatou
Original Paper
  • 135 Downloads

Abstract

A paired dominating set of a graph G with no isolated vertex is a dominating set S of vertices such that the subgraph induced by S in G has a perfect matching. The paired domination number of G, denoted by γ pr(G), is the minimum cardinality of a paired dominating set of G. The paired domination subdivision number \({{\rm sd}_{\gamma _{\rm pr}}(G)}\) is the minimum number of edges to be subdivided (each edge of G can be subdivided at most once) in order to increase the paired domination number. In this paper, we show that if G is a connected graph of order at least 4, then \({{\rm sd}_{\gamma _{\rm pr}}(G)\leq 2|V(G)|-5}\). We also characterize trees T such that \({{\rm sd}_{\gamma _{\rm pr}}(T) \geq |V(T)| /2}\).

Keywords

Paired domination number Paired domination subdivision number Tree 

Mathematics Subject Classification

05C69 

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Copyright information

© Springer 2012

Authors and Affiliations

  • Yoshimi Egawa
    • 1
  • Michitaka Furuya
    • 1
  • Masanori Takatou
    • 1
  1. 1.Department of Mathematical Information ScienceTokyo University of ScienceTokyoJapan

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