The Merrifield-Simmons Index of Two Classes of Silicate Molecular Graphs

Graph theory is of great use in modeling chemistry structures. In chemistry and physics, the silicate are the largest, the most interesting and the most completed class of minerals, and are the component of the common rock-forming minerals. The tetrahedron SiO4 is fundamental unit of silicates. The corner vertices are oxygen atoms and the center atom is the silicon atom. In this paper, we compute the Merrifield-Simmons index of two classes of silicate molecular graphs. We also show that these two classed molecular have the same independence entropy. The difference of matching entropy and the independence entropy is (log 2)/3.