The Wiener index of a graph is the sum of the distances between all pairs of vertices, it has
been one of the main descriptors that correlate a chemical compound's molecular graph with …

The number of subtrees in a graph is related to the reliability of a network with possible
vertex failure and edge failure. It is known that networks with larger number of subtrees …

Conditional independence and graphical models are well studied for probability
distributions on product spaces. We propose a new notion of conditional independence for …

In this paper, we solve the well-known symbolic regression problem that has been
intensively studied and has a wide range of applications. To solve it, we propose an efficient …

The extremal questions of maximizing or minimizing various distance-based graph
invariants among trees with a given degree sequence have been vigorously studied. In …

This article investigates some properties of the number of subtrees of a tree with given
degree sequence. These results are used to characterize trees with the given degree …

Combinatorial optimization is a fascinating topic. Combinatorial optimization problems arise
in a wide variety of important fields such as transportation, telecommunications, computer …

The subtree number index STN (G) of a simple graph G is the number of nonempty subtrees
of G. It is a structural and counting topological index that has received more and more …

Let T be a weighted tree. The weight of a subtree T1 of T is defined as the product of weights
of vertices and edges of T1. We obtain a linear-time algorithm to count the sum of weights of …

The number of subtrees of a graph and its variations are among popular topological indices
that have been vigorously studied. We investigate the subtree numbers of spiro and …