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Upper Bounds on the Paired Domination Subdivision Number of a Graph

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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 \({{\rm sd}_{\gamma _{\rm pr}}(T) \geq |V(T)| /2}\).

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Authors and Affiliations

  1. Department of Mathematical Information Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo, 162-8601, Japan

    Yoshimi Egawa, Michitaka Furuya & Masanori Takatou

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  1. Yoshimi Egawa
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  2. Michitaka Furuya
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  3. Masanori Takatou
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Correspondence to Michitaka Furuya.

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Egawa, Y., Furuya, M. & Takatou, M. Upper Bounds on the Paired Domination Subdivision Number of a Graph. Graphs and Combinatorics 29, 843–856 (2013). https://doi.org/10.1007/s00373-012-1162-2

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  • DOI: https://doi.org/10.1007/s00373-012-1162-2

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