On vertex and edge degree-based topological indices

Abstract

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.

Keywords

• entire topological index
• vertex and edge degree-based graph invariant
• degree (of vertex)
• degree (of edge)