Lower bound for the spectral radius of the starlike trees

A tree is a connected acyclic graph. A tree is called a starlike if exactly one of its vertices has degree greater than two. Let λι be the largest eigenvalue of the adjacency matrix of a starlike tree. In this work, we obtain a lower bound for the spectral radius of a starlike tree. This bound only depends of the maximum degree of the vertices.

Upper bound for the energy of the starlike trees

The energy graph was defined by Gutman, in 1978, as the sum of the absolute values of the eigenvalues of the adjacency matrix. In this work, we obtain a upper bound for the energy of a starlike tree. This bound is obtained in function of the number of vertices and the maximum degree of the vertices.

Pharmacological Characteristics Analysis of Two Molecular Structures

Each year a large number of new diseases were found worldwide, which requires the development of new drugs to cure these diseases. In this process, researchers need to do a lot of work to test the effectiveness of new drugs and side effects. Due to the intrinsic connection between the characteristics of compound and its molecular structure, methods of pharmaceutical theory are widely used in the analysis of the features of the drug. By calculating the chemical indices of drug molecular structure, scientists could learn the chemistry and pharmacy characteristics of the corresponding drugs. In this paper, from the theoretical perspective, we state the following conclusions: (1) the exact expression of generalized degree distance for starlike tree is determined; (2) the eccentricity related indices of hetrofunctional dendrimer are discussed. The results obtained have broad application prospects in the pharmaceutical sciences.

The bondage number of the strong product of a complete graph with a path and a special starlike tree

The bondage number [Formula: see text] of a graph [Formula: see text] is the cardinality of a minimum edge set whose removal from [Formula: see text] results in a graph with the domination number greater than that of [Formula: see text]. It is a parameter to measure the vulnerability of a communication network under link failure. In this paper, we obtain the exact value of the bondage number of the strong product of a complete graph and a path. That is, for any two integers [Formula: see text] and [Formula: see text], [Formula: see text] if [Formula: see text]; [Formula: see text] if [Formula: see text] (mod 3); [Formula: see text] if [Formula: see text] (mod 3). Furthermore, we determine the exact value of the bondage number of the strong product of a complete graph and a special starlike tree.