Sharp bounds on some distance-based graph invariants of n-vertex k-trees are established in a unified approach, which may be viewed as the weighted Wiener index or weighted Harary index. The main techniques used in this paper are graph transformations and mathematical induction. Our results demonstrate that among k-trees with n vertices the extremal graphs with the maximal and the second maximal reciprocal sum-degree distance are coincident with graphs having the maximal and the second maximal reciprocal product-degree distance (and similarly, the extremal graphs with the minimal and the second minimal degree distance are coincident with graphs having the minimal and the second minimal eccentricity distance sum).
The article is devoted to the discussions concerning economic growth and the environmental crisis that took place in Poland in the 1970s. The author focuses on two scientific conferences and the publications that accompanied them in order to analyse the questions of economic growth, science, technology, and consumption with regard to raising awareness of the ecological crisis. The reception of the Polish translation of The Limits to Growth is one of the questions discussed more specifically in the article. The main purpose of the article is to amend the ecological dimension of socialist thought and to reconstruct the main tensions and contradictions between the ecological and productivist tendencies within socialist ideology. The author analyses these questions in the context of degrowth theory and with regard to the current climate and ecological crisis.