on vertex and edge degree-based topological indices

Introduction/purpose: the entire topological indices (t ient) are a class of graph invariants depending on the degrees of vertices and edges. some general properties of these invariants are established. methods: combinatorial graph theory is applied. results: a new general expression for t ient is obtained. for triangle-free and quadrangle-free graphs, this expression can be significantly simplified. conclusion: the paper contributes to the theory of vertex and edge degree-based graph invariants.