For \(k \in {\mathbb {N}},\) Ali et al. (Discrete Appl Math 160:1845-1850, 2012) introduce the Steiner k-Wiener index \(SW_{k}(G)=\sum _{S\in V(G)} d(S),\) where d(S) is the minimum size of a connected subgraph of G containing the vertices of S. The average Steiner k-distance \(\mu _{k}(G)\) of G is defined as \(\genfrac(){0.0pt}1{n}{k}^{-1} SW_{k}(G)\). In this paper, we give some upper bounds on \(SW_{k}(G)\) and \(\mu _{k}(G)\) in terms of minimum degree, maximum degree and girth in a triangle-free or a \(C_{4}\)-free graph.

对于\(k \in {\mathbb {N}},\) Ali 等人。(Discrete Appl Math 160:1845-1850, 2012) 引入 Steiner k -Wiener 指数\(SW_{k}(G)=\sum _{S\in V(G)} d(S),\)其中d ( S ) 是G的包含S的顶点的连通子图的最小尺寸。G的平均 Steiner k距离 \(\mu _{k}( G )\)定义为\ (\ genfrac (){0.0pt}1{n}{k}^{-1} SW_{k} (G)\)。在本文中，我们给出了\(SW_{k}(G)\)和\(\mu _{k}(G)\)的一些上限就无三角形或\(C_{4}\)无图的最小度数、最大度数和周长而言。