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

摘要

A (n, n + 1)-graph G is a connected simple graph with n vertices and n + 1 edges. If d v denotes the degree of the vertex v, then the zeroth-order general Randi? index $R_alpha^0(G)$ of the graph G is defined as $sumnolimits_{vin V(G)}d_v^alpha$ , where α is a real number. We characterize, for any α, the (n,n + 1)-graphs with the smallest and greatest zeroth-order general Randi? index.