| Summary: | A Topological index also known as connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randić, atom-bond connectivity (ABC) and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study HDCN1(m,n) and HDCN2(m,n) of dimension <inline-formula> <math display="inline"> <semantics> <mrow> <mi>m</mi> <mo>,</mo> <mi>n</mi> </mrow> </semantics> </math> </inline-formula> and derive analytical closed results of general Randić index <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>R</mi> <mi>α</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="script">G</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> for different values of <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>. We also compute the general first Zagreb, ABC, GA, <inline-formula> <math display="inline"> <semantics> <mrow> <mi>A</mi> <mi>B</mi> <msub> <mi>C</mi> <mn>4</mn> </msub> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>G</mi> <msub> <mi>A</mi> <mn>5</mn> </msub> </mrow> </semantics> </math> </inline-formula> indices for these Hex derived cage networks for the first time and give closed formulas of these degree-based indices.
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