Abstract
There are many network topology designs that have emerged to fulfill the growing need for networks to provide a robust platform for a wide range of applications like running businesses and managing emergencies. Amongst the most famous network topology designs are star network, mesh network, hexagonal network, honeycomb network, etc. In a star network, a central computer is linked with various terminals and other computers over point-to-point lines. The other computers and terminals are directly connected to the central computer but not to one another. As such, any failure in the central computer will result in a failure of the entire network and computers in star network will not be able to communicate. The star topology design can be represented by a graph where vertices represent the computer nodes and edges represent the links between the computer nodes. In this paper, we study the vertex-edge-based topological descriptor for a newly designed hexagon star network.
Highlights
A topological index is a numeric amount related with a chemical constitution asserting a connection between chemical structures with numerous physicosynthetic properties and chemical reactivity
Topological indices are planned with the possibility of change of a chemical structure into a number that portrays the geography of that structure
Hexagonal networks are based on triangular plane tessellation or the partition of a plane into equilateral triangles provided that each node has up to six neighbors. e closest networks, in terms of design and structure, are those based on regular hexagons, called honeycomb networks. ose based on a regular square partition are called mesh networks [31, 32]
Summary
Let E and V be the edge set and vertex set of a simple connected graph G (V, E). e degree of a vertex θ, denoted by Ψ(θ), is the number of edges that are incident to θ. e open neighborhood of a vertex θ, denoted by N(θ), is a number of all vertices adjacent to θ. e closed neighborhood of θ, denoted by N[θ], is the union of θ and N(θ). Let E and V be the edge set and vertex set of a simple connected graph G (V, E). E degree of a vertex θ, denoted by Ψ(θ), is the number of edges that are incident to θ. E open neighborhood of a vertex θ, denoted by N(θ), is a number of all vertices adjacent to θ. E closed neighborhood of θ, denoted by N[θ], is the union of θ and N(θ). E ev-degree, denoted by Ψev(e), of any edge e θθ ∈ E is the total number of vertices of the closed neighborhood union of θ and θ. E ve-degree, denoted by Ψve(θ), of any vertex θ ∈ V is the number of different edges that are incident to any vertex from the closed neighborhood of θ. E ve-degree- and ev-degreebased topological indices are defined in the following equations. Equations (1)–(10) are known as ev-degree Zagreb α index, first ve-degree Zagreb α index, first ve-degree Zagreb β index, second ve-degree Zagreb index, ve-degree Randic index, ev-degree Randic index, ve-degree atom-bond connectivity index, ve-degree geometric-arithmetic index, ve-degree harmonic index, and ve-degree sum-connectivity index, respectively
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