A study on the reverse Euler Sombor index of various graphs

Abstract In this paper an attempt to define vertex degree-based topological index, reverse Euler Sombor index is made and established its mathematical properties. Reverse Euler Sombor index (REU (G) =ₔₕ ₄ (₆) (-dᵤ+1) ²+ (-dᵥ+1) ²+ (-dᵤ+1) (-dᵥ+1), where cᵤ=-dᵤ+1 for any vertex u V (G) and is the maximum vertex degree of the graph G) of standard graphs like path, cycle, complete, crown, star, wheel, friendship, ladder, butterfly, complete bipartite, helm, regular are determined. The bounds of reverse Euler Sombor index are found using famous Cauchy-Schwarz inequality and Jensen inequality. This study is extended for computing reverse Euler Sombor index for family of thorn graphs.