Euler Sombor Index of Trees, Unicyclic and Chemical Graphs

Recently, Tang et al. observed the chemical applicability of the Euler Sombor index, is potentially a very good molecular descriptor since it correlates well with the properties of octane isomers.For a simple graph G, the Euler Sombor index is defined aswhere a b means that the vertices a and b are adjacent and da represent the degree of the vertex a in G. Here, we obtain the family of trees with the first, second, third, fourth and fifth minimum Euler Sombor indices, unicyclic graphs with the maximum and first, second and third minimum Euler Sombor indices.Also, based on the Euler Sombor index, we classify the graphs extremal over chemical graphs and hexagonal systems.