Extremal Trees for the Exponential of Forgotten Topological Index

Abstract

Let F be the forgotten topological index of a graph G. The exponential of the forgotten topological index is defined as e(F)(G) = sigma((x,y)is an element of S)t(x,y)(G)e((x2+y2)), where t(x,y)(G) is the number of edges joining vertices of degree x and y. Let T-n be the set of trees with n vertices; then, in this paper, we will show that the path P-n has the minimum value for e(F) over T-n.