On Sombor index and graph energy of some chemically important graphs

Sombor index of a graph $G=(V\left(G\right),E\left(G\right))$ is provided by the expression ${\sum }_{uv\in E\left(G\right)}\sqrt{d_u^2+d_v^2}$, where $d_x$ is the degree of the vertex $x\in V\left(G\right)$. The energy of a graph is the quantity given by the total of the absolute values of its adjacency matrix’s eigenvalues. In this article, we improve the relation between the Sombor index and graph energy and derive the relation between them for unicyclic, bicyclic and tricyclic graphs, trees, triangular chain, square cactus chain and hexagonal cactus chain graphs. At last, we find the bounds of graph energy for zigzag and linear hexagonal chains.