20.500.12556/DiRROS-23893 Weighted Padovan graphs 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. Padovan sequence weighted Padovan graph integer partition median graphs Padovanovo zaporedje uteženi Padovanov graf particije medianski grafi true false true Angleški jezik Slovenski jezik Neznano 2025-10-20 11:20:30 2025-10-20 11:20:30 2025-10-24 03:55:14 0000-00-00 00:00:00 2025 0 0 12 str. iss. 7, article no. 114457 Vol. 348 Jul. 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-07-01 519.17 0012-365X 10.1016/j.disc.2025.114457 227687939 1-s2.0-S0012365X25000652-main.pdf 1-s2.0-S0012365X25000652-main.pdf 1 A4640CC8404E1A49793F08AE42884DCF 2acc06e79a34872b2ff04136c97401c4c09738ffab8a8abf52dbfca7372e82f2 3c751476-ad9a-11f0-9bb7-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=35450 https://www.sciencedirect.com/science/article/pii/S0012365X25000652 1 109a8bd0-ad96-11f0-9bb7-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=35449 Inštitut za matematiko, fiziko in mehaniko 0 0 0