On some distance-regular graphs with many vertices
نویسندگان
چکیده
منابع مشابه
Some Notes on Distance-Transitive and Distance-Regular Graphs
These are notes from lectures given in the Queen Mary Combinatorics Study 1 Introductory Definitions In these notes, Γ = (V Γ, EΓ) denotes a graph, as we will use G to denote a group. All graphs considered will be simple, finite, connected and undirected. Definition An automorphism of Γ is a bijective function g : V Γ → V Γ such that v ∼ w if and only if g(v) ∼ g(w). The set of all automorphism...
متن کاملSpectral Characterizations of Some Distance-Regular Graphs
When can one see from the spectrum of a graph whether it is distance-regular or not? We give some new results for when this is the case. As a consequence we find (among others) that the following distance-regular graphs are uniquely determined by their spectrum: The collinearity graphs of the generalized octagons of order (2, 1), (3, 1) and (4, 1), the Biggs-Smith graph, the M22 graph, and the ...
متن کاملDrawing Planar Graphs with Many Collinear Vertices
Given a planar graph G, what is the maximum number of collinear vertices in a planar straight-line drawing of G? This problem resides at the core of several graph drawing problems, including universal point subsets, untangling, and column planarity. The following results are known: Every n-vertex planar graph has a planar straight-line drawing with Ω( √ n) collinear vertices; for every n, there...
متن کاملSome Results on the Eigenvalues of Distance-Regular Graphs
In 1986, Terwilliger showed that there is a strong relation between the eigenvalues of a distance-regular graph and the eigenvalues of a local graph. In particular, he showed that the eigenvalues of a local graph are bounded in terms of the eigenvalues of a distance-regular graph, and he also showed that if an eigenvalue θ of the distance-regular graph has multiplicity m less than its valency k...
متن کاملSome Formulas for Spin Models on Distance-Regular Graphs
A spin model is a square matrix W satisfying certain conditions which ensure that it yields an invariant of knots and links via a statistical mechanical construction of V. F. R. Jones. Recently F. Jaeger gave a topological construction for each spin model W of an association scheme which contains W in its Bose Mesner algebra. Shortly thereafter, K. Nomura gave a simple algebraic construction of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2019
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-019-00888-5