On the sum of powers of vertex degrees of polycyclic graphs - Gutman, Ivan (Vojnotehnički glasnik / Military Technical Courier, 2025)
Introduction/purpose: The sum of powers of vertex degrees of graphs is much studied in the literature, but only for some fixed values of the power. General properties of these sums are studied to a much less extent. In this paper we offer results along these lines.Methods: Combinatorial graph theory is applied.Results: A few lower bounds for the sum of powers of vertex degrees are established, applicable to all powers. Classes of polycyclic graphs with minimum sum of powers of vertex degrees are characterized. Conclusion: The paper contributes to the study of the sum of powers of vertex degrees of graphs.
Keywords: degree (of vertex), sum of powers of vertex degrees of graphs, polycyclic graphs.