On Some Properties of Multiplicative Topological Indices in Silicon-Carbon
Abid Mahboob, Sajid Mahboob, Mohammed M. M. Jaradat, Nigait Nigar, Imran Siddique
Abstract
The use of graph theory can be visualized in nanochemistry, computer networks, Google maps, and molecular graph which are common areas to elaborate application of this subject. In nanochemistry, a numeric number (topological index) is used to estimate the biological, physical, and structural properties of chemical compounds that are associated with the chemical graph. In this paper, we compute the first and second multiplicative Zagreb indices ( <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:mn>1</a:mn> </a:mrow> </a:msub> <a:mfenced open="(" close=")" separators="|"> <a:mrow> <a:mi>G</a:mi> </a:mrow> </a:mfenced> </a:math> and ( <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" id="M2"> <f:msub> <f:mrow> <f:mi>M</f:mi> </f:mrow> <f:mrow> <f:mn>1</f:mn> </f:mrow> </f:msub> <f:mfenced open="(" close=")" separators="|"> <f:mrow> <f:mi>G</f:mi> </f:mrow> </f:mfenced> </f:math> )), generalized multiplicative geometric arithmetic index ( <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" id="M3"> <k:msup> <k:mrow> <k:mtext>GA</k:mtext> </k:mrow> <k:mrow> <k:mi>α</k:mi> </k:mrow> </k:msup> <k:mtext>II</k:mtext> <k:mfenced open="(" close=")" separators="|"> <k:mrow> <k:mi>G</k:mi> </k:mrow> </k:mfenced> </k:math> ), and multiplicative sum connectivity and multiplicative product connectivity indices ( <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" id="M4"> <p:mtext>SCII</p:mtext> <p:mfenced open="(" close=")" separators="|"> <p:mrow> <p:mi>G</p:mi> </p:mrow> </p:mfenced> </p:math> and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" id="M5"> <u:mtext>PCII</u:mtext> <u:mfenced open="(" close=")" separators="|"> <u:mrow> <u:mi>G</u:mi> </u:mrow> </u:mfenced> </u:math> ) of <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" id="M6"> <z:msub> <z:mrow> <z:mtext>SiC</z:mtext> </z:mrow> <z:mrow> <z:mn>4</z:mn> </z:mrow> </z:msub> <z:mo>−</z:mo> <z:mi>I</z:mi> <z:mfenced open="[" close="]" separators="|"> <z:mrow> <z:mi>m</z:mi> <z:mo>,</z:mo> <z:mi>n</z:mi> </z:mrow> </z:mfenced> </z:math> and <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" id="M7"> <eb:msub> <eb:mrow> <eb:mtext>SiC</eb:mtext> </eb:mrow> <eb:mrow> <eb:mn>4</eb:mn> </eb:mrow> </eb:msub> <eb:mo>−</eb:mo> <eb:mtext>II</eb:mtext> <eb:mfenced open="[" close="]" separators="|"> <eb:mrow> <eb:mi>m</eb:mi> <eb:mo>,</eb:mo> <eb:mi>n</eb:mi> </eb:mrow> </eb:mfenced> </eb:math> .