On Molecular Graphs with Valencies 1, 2 and 4 with Prescribed Numbers of Bonds

In this paper, necessary and sufficient conditions are given for the existence of molecular graph(s) with the prescribed sequence m11, m12, m14, m22, m24, m44, where mij denotes the number of edges (bonds) connecting vertices (atoms) of degree i with vertices of degree j. The main result expressed as Theorem 1 covers the great variety of molecules with valencies 1, 2 and 4