In quantitative structure-property and structure-activity relationships studies, several graph invariants, namely, topological indices have been defined and studied due to their numerous applications in computer networks, biotechnology, and nanochemistry. Topological indices are numeric parameters that describe the biological, physical, and chemical properties depending on the structure and topology of different chemical compounds. In this article, we inaugurated some degree-based novel indices, namely, geometric-harmonic
GHI
, harmonic-geometric
HGI
, neighborhood harmonic-geometric
NHGI
, and neighborhood geometric-harmonic
NGHI
indices and verified their chemical applicability. Furthermore, an attempt is made to calculate analytical closed formulas for different variants of silicon carbides and analyze the obtained results graphically.