2018
DOI: 10.1080/23799927.2018.1441186
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A note on the Steiner -diameter of a graph

Abstract: The Steiner distance of a graph, introduced by Chartrand, Oellermann, Tian and Zou in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph G of order at least 2 and S ⊆ V (G), the Steiner distance d(S) among the vertices of S is the minimum size among all connected subgraphs whose vertex sets contain S. Let n and k be two integers with 2 ≤ k ≤ n. Then the Steiner k-eccentricityIn 2011, Chartrand, Okamoto, Zhang showed that k − 1 ≤ sdiam k (G) ≤ n − 1. In this pape… Show more

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Cited by 7 publications
(6 citation statements)
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“…Let n and k be integers such that 2 ≤ k ≤ n. The Steiner k-eccentricity e Mao [18] obtained the following results. By ∆(G) we denote the maximum degree among all vertices of G.…”
Section: Distance and Its Generalizationmentioning
confidence: 99%
“…Let n and k be integers such that 2 ≤ k ≤ n. The Steiner k-eccentricity e Mao [18] obtained the following results. By ∆(G) we denote the maximum degree among all vertices of G.…”
Section: Distance and Its Generalizationmentioning
confidence: 99%
“…Lemma 2.3 [30] Let G be a connected graph of order n (n ≥ 3). Then sdiam 3 (G) = n−1 if and only if G satisfies one of the following conditions.…”
Section: Preliminariesmentioning
confidence: 99%
“…Later, Ali, Dankelmann, Mukwembi [2] improved the bound of sdiam k (G) and showed that sdiam k (G) ≤ 3n δ+1 + 2k − 5 for all connected graphs G. Moreover, they constructed graphs to show that the bounds are asymptotically best possible. In [36], Mao obtained the Nordhaus-Gaddum-type results for the parameter sdiam k (G).…”
Section: Classical Distance Parameters Steiner Distance Parametersmentioning
confidence: 99%
“…Mao et al[36] derived the following results for Steiner (n − 3)-diameter.Lemma 4.1 [36] Let G be a connected graph of order n. Then sdiam n−3 (G) = n − 4 if and only if κ(G) ≥ 4, and sdiam n−3 (G) = n − 1 if and only if G contains at least 3 cut vertices. Wang et al [50] obtained the structural properties of graphs with sdiam k (G) = n − Lemma Let k, n be two integers with 3 ≤ k ≤ n − 1.…”
mentioning
confidence: 99%