Some Mathematical Properties of Sombor Indices for Regular Graphs

Source abstract

In 2021, Gutman introduced Sombor index (SO) of a graph G and defined as SO(G)=∑_(uv∈E(G))▒√(〖deg⁡(u)〗^2+deg(v)^2 ) . In this paper, we have calculated the Sombor index of r-regular graph G_r, line graph of G_r, 〖L(G〗_r) and complement graph of G_r, (G_r ) ̅. We have also discussed a particular case of regular graphs, generalized Petersen graph P(s,t), its line graph L((P(s,t)) and complement graph (P(s,t)) ̅ for s>4 . We have proved the relation between these graphs and categorized them on the base of the Sombor index.