On the Wiener index of generalized Fibonacci cubes and Lucas cubes

DOI10.1016/j.dam.2015.02.002zbMath1315.05044OpenAlexW2063143623MaRDI QIDQ2348065

Yoomi Rho, Sandi Klavžar

Publication date: 10 June 2015

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.dam.2015.02.002

zbMATH Keywords

hypercubeisometric embeddingWiener indexgeneralized Fibonacci cubegeneralized Lucas cube

Mathematics Subject Classification ID

Hypergraphs (05C65) Distance in graphs (05C12) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60)

Related Items (14)

A negative answer to a problem on generalized Fibonacci cubes ⋮ The vertex version of weighted Wiener number for bicyclic molecular structures ⋮ The structures of bad words ⋮ On a novel eccentricity-based invariant of a graph ⋮ The self-concatenation of isometric strings is isometric ⋮ All good (bad) words consisting of 5 blocks ⋮ Infinite families of 2-isometric and not 3-isometric binary words ⋮ Enumerative properties and cube polynomials of Tribonacci cubes ⋮ A characterization of non-isometric binary words ⋮ Proof of a conjecture on 2-isometric words ⋮ Sum of weighted distances in trees ⋮ The (non-)existence of perfect codes in Fibonacci cubes ⋮ Tree with maximum non-self-centrality number among all trees of fixed order and maximum degree ⋮ Circular embeddability of isometric words

Uses Software

• Mathematica
• OEIS
• CFSum

Cites Work

• On the Wiener index of random trees
• Asymptotic number of isometric generalized Fibonacci cubes
• Generalized Fibonacci cubes
• Wiener index of hexagonal systems
• Wiener index versus Szeged index in networks
• Structure of Fibonacci cubes: a survey
• Wiener index in weighted graphs via unification of \(\varTheta^\ast\)-classes
• Generalized Lucas cubes
• Closed form summation of 𝐶-finite sequences
• Average distance and vertex-connectivity
• Generalized fibonacci cubes are mostly hamiltonian
• Wiener index of iterated line graphs of trees homeomorphic to the claw K_1,3
• Wiener index of trees: Theory and applications
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