On the Minimum General Sum-Connectivity of Trees of Fixed Order and Pendent Vertices

For a graph G, its general sum-connectivity is usually denoted by chi(alpha)(G) and is defined as the sum of the numbers [d(G)(u)+d(G)(v)(alpha) over all edges uv of G, where d(G)(u),d(G)(v) represent degrees of the vertices u,v, respectively, and alpha is a real number. This paper addresses the problem of finding graphs possessing the minimum chi(alpha) value over the class of all trees with a fixed order n and fixed number of pendent vertices n1 for alpha > 1. This problem is solved here for the case when 4 <= n(1)<=(n+5)/3 and alpha > 1, by deriving a lower bound on chi(alpha) for trees in terms of their orders and number of pendent vertices.