Weighted Padovan graphs
Vesna Ir\v{s}i\v{c} Chenoweth, Sandi Klav\v{z}ar, Gregor Rus, Elif Tan

TL;DR
This paper introduces weighted Padovan graphs based on Padovan words, analyzes their structural properties, and proves they are median graphs, expanding understanding of their combinatorial and algebraic features.
Contribution
The paper defines weighted Padovan graphs, explores their properties, and proves they are median graphs, providing new insights into their structure and symmetries.
Findings
Determined order, size, degree, diameter, cube polynomial, automorphism group.
Presented two isomorphic families of weighted Padovan graphs.
Proved that weighted Padovan graphs are median graphs.
Abstract
Weighted Padovan graphs , , , are introduced as the graphs whose vertices are all Padovan words of length with s, two vertices being adjacent if one can be obtained from the other by replacing exactly one with a . By definition, , where is the th Padovan number. Two families of graphs isomorphic to weighted Padovan graphs are presented. The order, the size, the degree, the diameter, the cube polynomial, and the automorphism group of weighted Padovan graphs are determined. It is also proved that they are median graphs.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGraph theory and applications · Advanced Graph Theory Research · Graph Labeling and Dimension Problems
