Sharp bounds of the zeroth-order general Randi? index of bicyclic graphs with given pendent vertices ?
Let G G be a simple connected graph and ? ? be a given real number. The zeroth-order general Randi? index of 0R?(G) 0 R ? ( G ) is defined as ?v?V(G)[dG(v)]? ? v ? V ( G ) [ d G ( v ) ] ? , where dG(v) d G ( v ) denotes the degree of the vertex v v of G G . In this paper, for any ?(?0,1) ? ( ? 0 , 1 ) , we give sharp bounds of the zeroth-order general Randi? index 0R? 0 R ? of all bicyclic graphs with n n vertices and k k pendent vertices.
sharp bound zeroth-order general randi? index bicyclic graph pendent vertex