2014
DOI: 10.1016/j.disc.2013.11.020
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Relating the annihilation number and the 2-domination number of a tree

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Cited by 15 publications
(14 citation statements)
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“…A similar result was proved by Desormeaux, Henning, Rall, and Yeo [6] for the 2domination number of trees. Very recently, a different proof was given for the same statement by Lyle and Patterson [10].…”
Section: Theorem 12 ([5]supporting
confidence: 84%
“…A similar result was proved by Desormeaux, Henning, Rall, and Yeo [6] for the 2domination number of trees. Very recently, a different proof was given for the same statement by Lyle and Patterson [10].…”
Section: Theorem 12 ([5]supporting
confidence: 84%
“…Many known bounds on the domination number and the independence number depend only on the degree sequence, or on derived quantities such as the order, the size, the minimum degree, and the maximum degree . For a graph G with nonincreasing degree sequence d=(d1,,dn), Slater observed γ(G)s(d) where sfalse(dfalse)=min0truekfalse[nfalse]:i=1kdink,and Pepper observed α(G)a(d) where afalse(dfalse)=max0trueafalse[nfalse]:i=na+1ndii=1nadi=nmin0truekfalse[nfalse]:i=1kdii=k+1ndiis known as the annihilation number of G . Clearly, γtrueprefixminfalse(dfalse)sfalse(dfalse) and αtrueprefixmaxfalse(dfalse)afalse(dfalse).…”
Section: Introductionmentioning
confidence: 99%
“…This was subsequently proven by Desormeaux et al (2014) in the case when T is a tree. The bound considered for this paper is motivated by this result.…”
Section: Introductionmentioning
confidence: 74%