Name
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 $$\\Gamma $$Γ be a graph with vertex set V, diameter D, adjacency matrix $$\\varvec{A}$$A, and adjacency algebra $$\\mathcal{A}$$A. Then, $$\\Gamma $$Γ is distance mean-regular when, for a given $$u\\in V$$uźV, the averages of the intersection numbers $$p_{ij}^h(u,v)=|\\Gamma _i(u)\\cap \\Gamma _j(v)|$$pijh(u,v)=|Γi(u)źΓj(v)| (number of vertices at distance i from u and distance j from v) computed over all vertices v at a given distance $$h\\in \\{0,1,\\ldots ,D\\}$$hź{0,1,ź,D} from u, do not depend on u. In this work we study some properties and characterizations of these graphs. For instance, it is shown that a distance mean-regular graph is always distance degree-regular, and we give a condition for the converse to be also true. Some algebraic and spectral properties of distance mean-regular graphs are also investigated. We show that, for distance mean regular-graphs, the role of the distance matrices of distance-regular graphs is played for the so-called distance mean-regular matrices. These matrices are computed from a sequence of orthogonal polynomials evaluated at the adjacency matrix of $$\\Gamma $$Γ and, hence, they generate a subalgebra of $$\\mathcal{A}$$A. Some other algebras associated to distance mean-regular graphs are also characterized. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/s10623-016-0208-5 | Des. Codes Cryptography |
Keywords | Field | DocType |
Distance-regular graph,Vertex-transitive graph,Distance mean-regular graph,Intersection mean-matrix,Adjacency Algebra,Spectrum,Interlacing,05E30,05C50 | Subalgebra,Adjacency matrix,Graph theory,Discrete mathematics,Combinatorics,Vertex-transitive graph,Vertex (geometry),Distance matrices in phylogeny,Matrix (mathematics),Distance-regular graph,Mathematics | Journal |
Volume | Issue | ISSN |
84 | 1-2 | 0925-1022 |
Citations | PageRank | References |
0 | 0.34 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| v diego | 1 | 0 | 0.34 |
| M. A. Fiol | 2 | 816 | 87.28 |