Study of Transformed <i>η^ζ</i> Networks via Zagreb Connection Indices

Abstract

A graph is a tool for designing a system’s required interconnection network. The topology of such networks determines their compatibility. For the first time, in this work we construct subdivided ηζ network S(ηζΓ) and discussed their topology. In graph theory, there are a variety of invariants to study the topology of a network, but topological indices are designed in such a way that these may transform the graph into a numeric value. In this work, we study S(ηζΓ) via Zagreb connection indices. Due to their predictive potential for enthalpy, entropy, and acentric factor, these indices gain value in the field of chemical graph theory in a very short time. ηζΓ formed by ζ time repeated process which consists ηζ copies of graph Γ along with η2|V(Γ)|ζηζ−1 edges which used to join these ηζ copies of Γ. The free hand to choose the initial graph Γ for desired network S(ηζΓ) and its relation with chemical networks along with the repute of Zagreb connection indices enhance the worth of this study. These computations are theoretically innovative and aid topological characterization of S(ηζΓ).

Keywords

• Zagreb connection indices
• mk graphs
• topological index
• network
• subdivided graph
• transformed graph