Hamiltonian index of directed multigraph

Juan Liu, Shupeng Li, Xindong Zhang and Hong-Jian Lai

Applied Mathematics and Computation, 2022, vol. 425, issue C

Abstract: The index of a property P for a directed multigraph D is the smallest nonnegative integer k such that the iterated line digraph Lk(D) has the property P. Let e(D) denote the eulerian index of D and h(D) denote the hamiltonian index of D. Directed multigraphs families F and H are defined such that a directed multigraph D has a finite value e(D) if and only if D∈F, and D has a finite value h(D) if and only if D∈F∪H. Furthermore, the values of the hamiltonian indices for members in F∪H are determined. In addition, line digraph stable properties are investigated, and sufficient and necessary conditions are obtained for a subfamily of strong directed multigraphs in which being eulerian and being hamiltonian are line digraph stable.

Keywords: Eulerian index; Hamiltonian index; Iterated line digraph; Line digraph stable property (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:425:y:2022:i:c:s0096300322001588

DOI: 10.1016/j.amc.2022.127074

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