Steiner diameter, maximum degree and size of a graph

Let G be a connected graph of order n . The Steiner distance d ( S ) set vertices is the minimum size subgraph that contains all For k ≤ , -diameter sdiam maximum among sets generalises classical diameter, which coincides with 2-diameter. problem determining given order, diameter and degree was first studied by Erdös Rényi. In this paper we consider corresponding for -diameter. Δ ∈ N define e as at most if such exists. study special case = 3 initiated in recent Mao. determine { − 1 2 } prove ⌈ 9 8 + ⌉ also ≥ 7 We further show for, approximately, log ⁡