On the first extended zeroth-order connectivity index of trees

Document Type: Regular Paper

Authors

1 2Department of Mathematics, South China Normal University, Guangzhou 510631, P. R. China

2 Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803-4918, USA

Abstract

The first extended zeroth-order connectivity index of a graph
 
G is defined as 0 1/2
1
( )
( ) ,
 
v
 
v V G
 

 
G D


 
where
 
V
 
(G) is the vertex set of G, and v D is the sum of degrees of neighbors of vertex v in G. We give a sharp
lower bound for the first extended zeroth-order connectivity index of trees with given numbers of vertices and
pendant vertices, and characterize the extremal trees. We also determine the
 
n-vertex trees with the first three
smallest first extended zeroth-order connectivity indices.

Keywords