Extremal (n,n+1)-graphs with respected to zeroth- order general Randic index

摘要

A ( n, n + 1)-graph G is a connected simple graph with n vertices and n + 1 edges. If d(upsilon) denotes the degree of the vertex v, then the zeroth-order general Randic index R-alpha(0)( G) of the graph G is defined as Sigma nu is an element of V( G) d(upsilon)(alpha), where a is a real number. We characterize, for any a, the ( n, n + 1)-graphs with the smallest and greatest zeroth-order general Randic index.