A Survey on D-bounded Distance-regular Graphs∗
نویسنده
چکیده
Ω is weak-geodetically closed whenever Ω is weak-geodetically closed with respect to w for any w ∈ X. ∗A manuscript for algebraic combinatorics workshop 7/2-4 in National Hsinchu University of Education, an extension of 2007 International Conference on Graph Theory and Combinatorics & Fourth Cross-strait Conference on Graph Theory and Combinatorics. †Department of Applied Mathematics, National Chiao Tung University, Taiwan R.O.C..
منابع مشابه
D-Spectrum and D-Energy of Complements of Iterated Line Graphs of Regular Graphs
The D-eigenvalues {µ1,…,µp} of a graph G are the eigenvalues of its distance matrix D and form its D-spectrum. The D-energy, ED(G) of G is given by ED (G) =∑i=1p |µi|. Two non cospectral graphs with respect to D are said to be D-equi energetic if they have the same D-energy. In this paper we show that if G is an r-regular graph on p vertices with 2r ≤ p - 1, then the complements of iterated lin...
متن کاملD - bounded Property in a Distance - regular Graph with a 1 = 0 and a 2 6 = 0
Let Γ denote a distance-regular graph with diameter D and intersection numbers a2 > a1 = 0. We show that for each 1 ≤ d ≤ D−1, if Γ contains no parallelograms of lengths up to d+1 then Γ is d-bounded in the sense of the article [D-bounded distance-regular graphs, European Journal of Combinatorics(1997)18, 211-229]. By applying this result we show the nonexistence of distance-regular graphs with...
متن کامل3-bounded Property in a Triangle-free Distance-regular Graph
Let Γ denote a distance-regular graph with classical parameters (D, b, α, β) and D ≥ 3. Assume the intersection numbers a1 = 0 and a2 6= 0. We show Γ is 3-bounded in the sense of the article [D-bounded distance-regular graphs, European Journal of Combinatorics(1997)18, 211-229].
متن کاملar X iv : 0 70 9 . 05 64 v 1 [ m at h . C O ] 5 S ep 2 00 7 3 - bounded Property in a Triangle - free Distance - regular Graph ∗
Let Γ denote a distance-regular graph with classical parameters (D, b, α, β) and D ≥ 3. Assume the intersection numbers a1 = 0 and a2 6= 0. We show Γ is 3-bounded in the sense of the article [D-bounded distance-regular graphs, European Journal of Combinatorics(1997)18, 211-229].
متن کاملAlgebraic characterizations of distance-regular graphs
We survey some old and some new characterizations of distance-regular graphs, which depend on information retrieved from their adjacency matrix. In particular, it is shown that a regular graph with d+ 1 distinct eigenvalues is distance-regular if and only if a numeric equality, involving only the spectrum of the graph and the numbers of vertices at distance d from each vertex, is satisfied.
متن کاملD-bounded Distance-regular Graphs
Let Γ = (X, R) denote a distance-regular graph with diameter D ≥ 3 and distance function δ. A (vertex) subgraph ∆ ⊆ X is said to be weak-geodetically closed whenever for all x, y ∈ ∆ and all z ∈ X, δ(x, z) + δ(z, y) ≤ δ(x, y) + 1 −→ z ∈ ∆. Γ is said to be D-bounded whenever for all x, y ∈ X, x, y are contained in a common regular weak-geodetically closed subgraph of diameter δ(x, y). Assume Γ i...
متن کامل