| Summary: | The study of the interconnections between chemical systems is known as chemical graph theory. Through the use of star graphs, a limited group of researchers has examined the space of possible solutions for boundary-value problems. They recognized that for their strategy to function, they needed a core node related to other nodes but not to itself; as a result, they opted to use star graphs. In this sense, the graphs of neopentane will be helpful in extending the scope of our technique. It has the CAS number 463-82-1 and the chemical formula <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>C</mi><mn>5</mn></msub><msub><mi>H</mi><mn>12</mn></msub></mrow></semantics></math></inline-formula>, and it is a component of a petrochemical precursor. In order to determine whether or not the suggested boundary-value problems on these graphs have any known solutions, we use the theorems developed by Schaefer and Krasnoselskii on fixed points. In addition, we illustrate our preliminary results with the help of an example that we present.
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