On Certain Aspects of Topological Indices
Tanweer Ul Islam, Zeeshan Saleem Mufti, Aqsa Ameen, Muhammad Nauman Aslam, Ali Tabraiz
Abstract
A topological index, also known as connectivity index, is a molecular structure descriptor calculated from a molecular graph of a chemical compound which characterizes its topology. Various topological indices are categorized based on their degree, distance, and spectrum. In this study, we calculated and analyzed the degree-based topological indices such as first general Zagreb index <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:msub> <a:mrow> <a:mi>M</a:mi> </a:mrow> <a:mrow> <a:mi>r</a:mi> </a:mrow> </a:msub> <a:mfenced open="(" close=")" separators="|"> <a:mrow> <a:mi>G</a:mi> </a:mrow> </a:mfenced> </a:math> , geometric arithmetic index <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" id="M2"> <f:mtext>GA</f:mtext> <f:mfenced open="(" close=")" separators="|"> <f:mrow> <f:mi>G</f:mi> </f:mrow> </f:mfenced> </f:math> , harmonic index <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" id="M3"> <k:mi>H</k:mi> <k:mfenced open="(" close=")" separators="|"> <k:mrow> <k:mi>G</k:mi> </k:mrow> </k:mfenced> </k:math> , general version of harmonic index <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" id="M4"> <p:msub> <p:mrow> <p:mi>H</p:mi> </p:mrow> <p:mrow> <p:mi>r</p:mi> </p:mrow> </p:msub> <p:mfenced open="(" close=")" separators="|"> <p:mrow> <p:mi>G</p:mi> </p:mrow> </p:mfenced> </p:math> , sum connectivity index <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" id="M5"> <u:mi>λ</u:mi> <u:mfenced open="(" close=")" separators="|"> <u:mrow> <u:mi>G</u:mi> </u:mrow> </u:mfenced> </u:math> , general sum connectivity index <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" id="M6"> <z:msub> <z:mrow> <z:mi>λ</z:mi> </z:mrow> <z:mrow> <z:mi>r</z:mi> </z:mrow> </z:msub> <z:mfenced open="(" close=")" separators="|"> <z:mrow> <z:mi>G</z:mi> </z:mrow> </z:mfenced> </z:math> , forgotten topological index <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" id="M7"> <eb:mi>F</eb:mi> <eb:mfenced open="(" close=")" separators="|"> <eb:mrow> <eb:mi>G</eb:mi> </eb:mrow> </eb:mfenced> </eb:math> , and many more for the Robertson apex graph. Additionally, we calculated the newly developed topological indices such as the <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" id="M8"> <jb:msub> <jb:mrow> <jb:mtext>AG</jb:mtext> </jb:mrow> <jb:mrow> <jb:mn>2</jb:mn> </jb:mrow> </jb:msub> <jb:mfenced open="(" close=")" separators="|"> <jb:mrow> <jb:mi>G</jb:mi> </jb:mrow> </jb:mfenced> </jb:math> and Sanskruti index for the Robertson apex graph G.