On forwarding indices of networks
Discrete Applied Mathematics
Chordal rings as fault-tolerant loops
Discrete Applied Mathematics - Special double volume: interconnection networks
A note on isomorphic chordal rings
Information Processing Letters
Automorphism groups, isomorphism, reconstruction
Handbook of combinatorics (vol. 2)
All-to-all optical routing in optimal chordal rings of degree four
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A Combinatorial Problem Related to Multimodule Memory Organizations
Journal of the ACM (JACM)
On isomorphisms of finite Cayley graphs: a survey
Discrete Mathematics
Survival Reliability of Some Double-Loop Networks and Chordal Rings
IEEE Transactions on Computers
Independent Spanning Trees of Chordal Rings
COCOON '97 Proceedings of the Third Annual International Conference on Computing and Combinatorics
| Hi-index | 0.04 |
This paper presents the main properties of chordal rings of degree 3. This family of graphs is strongly related to circulant graphs, which are actually often called chordal rings too. The use of triangles in the plane to represent the vertices allows one to associate a plane tessellation to every chordal ring. By using this geometrical approach, we study the recognition and the isomorphism problems for this class of graphs. A polynomial-time algorithm to recognize chordal rings and a polynomial-time algorithm to decide isomorphism between two chordal rings, given by its adjacency list, are presented. Both algorithms are based on the study of the 4- and 6-cycles of the graph. This approach is also applied to the characterization of the automorphisms-group of chordal rings. We believe that these results produce useful tools for further works as, in particular, the study of compact routing schemes, and the study of optical routing protocols in edge-transitive chordal rings.