| Summary: | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>η</mi><mi>ζ</mi></msup></semantics></math></inline-formula> network <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>(</mo><msup><mi>η</mi><mi>ζ</mi></msup><mi mathvariant="sans-serif">Γ</mi><mo>)</mo></mrow></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>(</mo><msup><mi>η</mi><mi>ζ</mi></msup><mi mathvariant="sans-serif">Γ</mi><mo>)</mo></mrow></semantics></math></inline-formula> 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. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>η</mi><mi>ζ</mi></msup><mi mathvariant="sans-serif">Γ</mi></mrow></semantics></math></inline-formula> formed by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ζ</mi></semantics></math></inline-formula> time repeated process which consists <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>η</mi><mi>ζ</mi></msup></semantics></math></inline-formula> copies of graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Γ</mi></semantics></math></inline-formula> along with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfenced separators="" open="(" close=")"><mfrac linethickness="0pt"><mi>η</mi><mn>2</mn></mfrac></mfenced><mrow><mo>|</mo><mi>V</mi><mrow><mo>(</mo><mi mathvariant="sans-serif">Γ</mi><mo>)</mo></mrow><mo>|</mo></mrow><mi>ζ</mi><msup><mi>η</mi><mrow><mi>ζ</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula> edges which used to join these <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>η</mi><mi>ζ</mi></msup></semantics></math></inline-formula> copies of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Γ</mi></semantics></math></inline-formula>. The free hand to choose the initial graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Γ</mi></semantics></math></inline-formula> for desired network <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>(</mo><msup><mi>η</mi><mi>ζ</mi></msup><mi mathvariant="sans-serif">Γ</mi><mo>)</mo></mrow></semantics></math></inline-formula> 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>(</mo><msup><mi>η</mi><mi>ζ</mi></msup><mi mathvariant="sans-serif">Γ</mi><mo>)</mo></mrow></semantics></math></inline-formula>.
|
|---|