We derive a number of upper and lower bounds for the first eigenvalue in several contexts: many of these estimates will be sharp, and for some of them we characterize equality.
If, then Theorem 1.1 is also true; otherwise, we repeat the above process again and denote and the greatest lower bounds for the first and the second variables, respectively.
In the following theorem we determine the lower and upper bounds for the first Zagreb, ABC, the third Zagreb, the augmented Zagreb, the first multiple Zagreb and GA indices of the Cartesian product of F-sum of graphs in terms of their factor graphs for (F=T).
In the following theorem we determine the lower and upper bounds for the first Zagreb, ABC, the third Zagreb, the augmented Zagreb, the first multiple Zagreb and GA indices of the Cartesian product of F-sum of graphs in terms of their factor graphs for (F=S) and (F=R).
So, we presented bounds for the first Zagreb index, the ABC-index, the third Zagreb index, the augmented Zagreb index, the F-index, the first multiple Zagreb index and the GA-index for the Cartesian product of F-sum of graphs in form of its factor graphs.
This section is meant for determination of bounds for the first Zagreb, the third Zagreb, the augmented Zagreb, the first multiple Zagreb, ABC and GA indices of the Cartesian product of F-sum of graphs in terms of their factor graphs.
Moreover, we find sharp bounds for the second and third coefficient in these classes.
The bounds for the second Hankel determinant H 2 ( 2 ) = a 2 a 4 − a 3 2 are obtained for functions belonging to these subclasses of Ma-Minda starlike and convex functions in Section 2.
Bound for the first of those tours, the group played aboard the Ile de France, along with the Mills Brothers, the Ballet Russe and others.
The Bobcats are playoff-bound for the first time in their six-year history, and Jordan has pledged his involvement in the form of $275 million.
