Can I read Weighted Padovan graphs on EtoBox?

Weighted Padovan graphs by Chenoweth, Vesna Iršič; Klavžar, Sandi; Rus, Gregor; Tan, Elif is a scholarly article available to read on EtoBox.

What is Weighted Padovan graphs about?

Weighted Padovan graphs $\Phi^{n}_{k}$, $n \geq 1$, $\lfloor \frac{n}{2} \rfloor \leq k \leq \lfloor \frac{2n-2}{3} \rfloor$, are introduced as the graphs whose vertices are all Padovan words of length $n$ with $k$ $1$s, two vertices being adjacent if one can be obtained from the other by replacing exactly one $01$ with a $10$. By definition, $\sum_k |V(\Phi^{n}_{k})|=P_{n+2}$, where $P_n$ is the $n$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.

Author

Chenoweth, Vesna Iršič; Klavžar, Sandi; Rus, Gregor; Tan, Elif

Published

2024

Language

EN