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Distance mean-regular graphs

Author
Diego, V.; Fiol, M.
Type of activity
Journal article
Journal
Designs codes and cryptography
Date of publication
2017-07
Volume
84
Number
1
First page
55
Last page
71
DOI
https://doi.org/10.1007/s10623-016-0208-5 Open in new window
Project funding
Optimization techniques in graph theory, groups, and combinatorics. Applications to networks, algorithms, and communication protocols
Repository
http://hdl.handle.net/2117/91052 Open in new window
URL
https://link.springer.com/article/10.1007%2Fs10623-016-0208-5 Open in new window
Abstract
We introduce the concept of distance mean-regular graph, which can be seen as a generalization of both vertex-transitive and distance-regular graphs. Let G be a graph with vertex set V , diameter D, adjacency matrix A, and adjacency algebra A. Then, G is distance mean-regular when, for a given u ¿ V , the averages of the intersection numbers p h ij (u, v) = |Gi(u) n Gj (v)| (number of vertices at distance i from u and distance j from v) computed over all vertices v at a given distance h ¿ {0, ...
Citation
Fiol, M., Diego, V. Distance mean-regular graphs. "Designs codes and cryptography", 2017, vol. 84, núm. 1, p. 55-71.
Keywords
Adjacency Algebra, Distance mean-regular graph, Distance-regular graph, Interlacing, Intersection mean-matrix, Spectrum, Vertex-transitive graph
Group of research
COMBGRAPH - Combinatorics, Graph Theory and Applications

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