Abstract
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
References
Proposed Creative Commons Copyright Notices
Proposed Policy for Military Technical Courier (Journals That Offer Open Access)
Authors who publish with this journal agree to the following terms:
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).