Bounding the paired-domination number of a tree in terms of its annihilation number
Keyword(s):
A paired-dominating set of a graph G=(V, E) with no isolated vertex is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number of G, denoted by ?pr(G), is the minimum cardinality of a paired-dominating set of G. The annihilation number a(G) is the largest integer k such that the sum of the first k terms of the non-decreasing degree sequence of G is at most the number of edges in G. In this paper, we prove that for any tree T of order n?2,?pr(T)? 4a(T)+2/3 and we characterize the trees achieving this bound.
2020 ◽
Vol 12
(06)
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pp. 2050072
2021 ◽
Vol vol. 23, no. 3
(Graph Theory)
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Keyword(s):
2020 ◽
Vol 12
(05)
◽
pp. 2050065
2019 ◽
Vol 11
(01)
◽
pp. 1950004
2017 ◽
Vol 09
(01)
◽
pp. 1750009
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Keyword(s):