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Chemical graph theory comprehends the basic properties of an atomic graph. The sub-atomic diagrams are the graphs that are comprised of particles called vertices and the covalent bond between them are called edges. The eccentricity <inline-formula> <math display="inline"> <semantics> <msub> <mi>ϵ</mi> <mi>u</mi> </msub> </semantics> </math> </inline-formula> of vertex <i>u</i> in an associated graph <i>G</i>, is the separation among <i>u</i> and a vertex farthermost from <i>u</i>. In this article, we consider the precious stone structure of cubic carbon and registered Eccentric-connectivity index <inline-formula> <math display="inline"> <semantics> <mrow> <mi>&#958;</mi> <mo>(</mo> <mi>G</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>, Eccentric connectivity polynomial <inline-formula> <math display="inline"> <semantics> <mrow> <mi>E</mi> <mi>C</mi> <mi>P</mi> <mo>(</mo> <mi>G</mi> <mo>,</mo> <mi>x</mi> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> and Connective Eccentric index <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>C</mi> <mi>&#958;</mi> </msup> <mrow> <mo>(</mo> <mi>G</mi> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> of gem structure of cubic carbon for <i>n</i>-levels.