Abstract
AbstractIt is known that there exists a Minimum Distance Diagram (MDD) for circulant digraphs of degree two (or double-loop computer networks) which is an L-shape. Its description provides the graph’s diameter and average distance on constant time. In this paper we clarify, justify and extend these diagrams to circulant digraphs of arbitrary degree by presenting monomial ideals as a natural tool. We obtain some properties of the ideals we are concerned. In particular, we prove that the corresponding MDD is also an L-shape in the affine r-dimensional space. We implement in PostScript language a graphic representation of MDDs for circulant digrahs with two or three jumps. Given the irredundant irreducible decomposition of the associated monomial ideal, we provide formulae to compute the diameter and the average distance. Finally, we present a new and attractive family (parametrized with the diameter d>2) of circulant digraphs of degree three associated to an irreducible monomial ideal.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
