Ordering Acyclic Connected Structures of Trees Having Greatest Degree-Based Invariants

Abstract

Being building block of data sciences, link prediction plays a vital role in revealing the hidden mechanisms that lead the networking dynamics. Since many techniques depending in vertex similarity and edge features were put forward to rule out many well-known link prediction challenges, many problems are still there just because of unique formulation characteristics of sparse networks. In this study, we applied some graph transformations and several inequalities to determine the greatest value of first and second Zagreb invariant, SK and SK1 invariants, for acyclic connected structures of given order, diameter, and pendant vertices. Also, we determined the corresponding extremal acyclic connected structures for these topological indices and provide an ordering (with 5 members) giving a sequence of acyclic connected structures having these indices from greatest in decreasing order.