A tree is an acyclic graph. In computer science, trees are used to represent data structures. The Tree is the fundamentally used theoretical model in various fields such as information theory, artificial intelligence, combinatorial optimization, operations research, and theory of electrical and design networks
In the field of Chemical graph theory, topological indices are an area of research that provides the physicochemical properties of different chemical structures, especially for drug compounds
Glued tree structure was introduced and is helpful in quantum walks. Also, the hyprtree structure has many applications such as in dendrimers and chemical compounds with heavy atoms. Being inspired by this, we developed a new interconnection network, Glued hypertree which can be more helpful in the transmission of signals in biological networks. By evaluating various distancebased topological descriptors, the physicochemical properties of the new network can be determined which can be used in shaping the properties of the same.
In this paper, we have introduced an interconnection network, Glued hypertree. Section
The basic skeleton for glued hypertree is a combination of hypertree, a complete binary tree, and a glued graph. Glued hypertree is formed by gluing two hypertrees of the same level. Refer to
Let us denote
Glued hypertree has
In this section, we did a comparative analysis on glued tree and glued hypertree. We used some topological parameters like average vertex degree, network cost, network throughput, average distance, message traffic density to analyze glued tree and glued hypertree. The number of nodes and diameter of the glued tree and glued hypertree is
The number of edges incident to a vertex is defined as vertex degree. The average vertex degree is the ratio of two times the number of edges to the number of vertices. The average vertex degree of the glued tree is
The network cost of a graph is the product of diameter and vertex degree. The network cost of the glued tree is
Network throughput is the ratio of total network bandwidth, proportional to the number of edges in the graph network to the diameter. For a glued tree of dimension
Topological indices are used to characterize physicochemical properties of chemical structures such as boiling point, melting point, octanol partition coefficients, vapor pressures, etc. The graph


Wiener^{ } 

Szeged^{ } 

Edge Szeged^{ } 

Edge vertex Szeged^{ } 

Mostar 

Edge Mostar 

Padmakar Ivan^{ } 

Consider
For a graph
where
where
•
•
•
We have used the same for calculating Mostar, edge Mostar, and total mostar indices.
Proof. First, we determine the
Consider a partition
In general,
The Wiener index of
where
The Szeged type indices of glued hypertree are calculated as follows:
Mostar indices of glued hypertree are calculated as shown below
We calculated the Padmakar Ivan index of glued hypertree also.
The average distance can be defined as the average sum of the distances between the pairs of vertices in a graph. Thus average distance can be derived from the Wiener index. The average distance of Glued tree and Glued Hypertree is
The message traffic density of a network is the ratio of the product of the average distance and number of nodes of the network to the number of links of the network. Message traffic density of Glued tree and Glued hypertree is
In the comparison of Glued hypertree with the Glued tree, Glued hypertree is a better interconnection network. The message traffic density of glued hypertree is less than that of higher internode communication performance. The network throughput is higher for glued hypertree, thus it maximizes the number of messages delivered per unit time through the network compared to glued tree. The distancebased indices give an overview of the topological properties of Glued hypertree. Thus this network can be used for future applications in the field of biology and chemistry like hypertrees
In this article, we introduced an interconnection network, Glued hypertree which is a better interconnection network than glued tree and discussed its properties. Some distancebased topological indices of Glued hypertree are also studied, giving us an idea about its physiochemical properties. The physiochemical of the glued hypertree gives an insight into the application of glued hypertree in various fields of science like predicting biological activities of various heavy metalbased chemical compounds and in computer science. In the future, we can evaluate eccentricitybased topological indices and also degreebased indices using Mpolynomials of glued hypertree.