Steiner 4-Diameter, Maximum Degree and Size of a Graph - Li, He; Zhang, Shumin; Zhu, Bo; Ye, Chengfu (Discontinuity, Nonlinearity, and Complexity, 2026)
The Steiner k-diameter sdiam_k(G) of a graph G, introduced by Chartrand, Oellermann, Tian and Zou in 1989, is a natural generalization of the concept of classical diameter. When k=2, sdiam_2(G)=diam(G) is the classical diameter. Let d, and n be natural numbers and dn, n. Denote by H_k(n,,d) the set of all graphs of order n with maximum degree and sdiam_k(G)≤ d. Let e_k(n,,d)={e(G):GH_k(n,,d)}. In this paper, we focus on the case k=4, and study the exact value of e_4(n,,d).