Distance-Hereditary Embeddings of Circulant Graphs
نویسندگان
چکیده
In this paper we present a distance-hereditary decomposition of optimal chordal rings of 2k nodes into a set of rings of 2k nodes, where k is the diameter. All the rings belonging to this set have the same length and their diameter corresponds to the diameter of the chordal ring in which they are embedded. The members of this embedded set of rings are non-disjoint and preserve the minimal routing of the original circulant graph. Besides its practical consequences, our research allows the presentation of these optimal circulant graphs as a particular evolution of the traditional ring topology.
منابع مشابه
On Embeddings of Circulant Graphs
A circulant of order n is a Cayley graph for the cyclic group Zn, and as such, admits a transitive action of Zn on its vertices. This paper concerns 2-cell embeddings of connected circulants on closed orientable surfaces. Embeddings on the sphere (the planar case) were classified by Heuberger (2003), and by a theorem of Thomassen (1991), there are only finitely many vertex-transitive graphs wit...
متن کاملGenus distributions of orientable embeddings for two types of graphs
Abstract On the basis of the joint tree model introduced by Liu in 2003, the genus distributions of the orientable embeddings for further types of graphs can be obtained. These are apparently not easily obtained using overlap matrices, the formula of Jackson, etc. In this paper, however, by classifying the associated surfaces, we calculate the genus distributions of the orientable embeddings fo...
متن کاملChordal Topologies for Interconnection Networks
The class of dense circulant graphs of degree four with optimal distance-related properties is analyzed in this paper. Two geometric characterizations are given, one in the plane and other in the space. Both characterizations facilitate the analysis of their topological properties and corroborate their suitability for implementing interconnection networks for distributed and parallel computers....
متن کاملDistance spectra and Distance energy of Integral Circulant Graphs
The distance energy of a graph G is a recently developed energy-type invariant, defined as the sum of absolute values of the eigenvalues of the distance matrix of G. There was a vast research for the pairs and families of non-cospectral graphs having equal distance energy, and most of these constructions were based on the join of graphs. A graph is called circulant if it is Cayley graph on the ...
متن کاملRecognizing Recursive Circulant Graphs G(cd M ; D)
Recursive circulant graphs G(N; d) have been introduced in 1994 by Park and Chwa PC94] as a new topology for interconnection networks. Recursive circulant graphs G(N; d) are circu-lant graphs with N nodes and with jumps of powers of d. A subfamily of recursive circulant graphs (more precisely, G(2 k ; 4)) is of same order and degree than the hypercube of dimension k, with sometimes better param...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003