Some Mathematical Properties of Sombor Indices for Regular Graphs
DOI:
https://doi.org/10.11113/mjfas.v20n6.3839Keywords:
Topological indices, Sombor index, regular graph, Petersen graph.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.
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Copyright (c) 2024 Muhammad Muhammad Rafiullah, Dur-E- Jabeen, Mohamad Nazri Husin
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