Horadam–Lucas Cubes
Year: 2024
Type: article
Abstract: In this paper, we introduce a novel class of graphs referred to as the Horadam–Lucas cubes. This class extends the concept of Lucas cubes and retains numerous desirable properties associated with them. Horadam–Lucas cubes can also be viewed as a companion graph family of the Horadam cubes, in a similar way the Lucas cubes relate to Fibonacci cubes or the Lucas-run graphs relate to Fibonacci-run graphs. As special cases, they also give rise to new graph families, such as Pell–Lucas cubes and Jacobsthal–Lucas cubes. We derive the several metric and enumerative properties of these cubes, including their diameter, periphery, radius, fundamental decomposition, number of edges, cube polynomials, and generating function of the cube polynomials.
Source: Axioms
Authors: Elif Tan, Luka Podrug, Vesna Iršič Chenoweth
Institutions: Ankara University, University of Zagreb, University of Ljubljana
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,728
Awards: Interplay of geometry, topology and algebra in structural and topological graph theory, Matchings, transversals, and hypergraphs, Graph theory, Investigation of edge general position problem in Fibonacci-like cubes, G5099342464, Metric Problems in Graphs and Hypergraphs, The game of Cops and Robber on graphs and geodesic spaces, G6311796530
OpenAlex ID: W4404821171