منابع مشابه
Parallelogram-Free Distance-Regular Graphs
Let 1=(X, R) denote a distance-regular graph with distance function and diameter d 4. By a parallelogram of length i (2 i d ), we mean a 4-tuple xyzu of vertices in X such that (x, y)= (z, u)=1, (x, u)=i, and (x, z)= ( y, z)= ( y, u)=i&1. We prove the following theorem. Theorem. Let 1 denote a distanceregular graph with diameter d 4, and intersection numbers a1=0, a2 {0. Suppose 1 is Q-polynomi...
متن کاملTriangle-free distance-regular graphs
Let Γ = (X, R) denote a distance-regular graph with distance function ∂ and diameter d ≥ 3. For 2 ≤ i ≤ d, by a parallelogram of length i, we mean a 4-tuple xyzu of vertices in X such that ∂(x, y) = ∂(z, u) = 1, ∂(x, u) = i, and ∂(x, z) = ∂(y, z) = ∂(y, u) = i − 1. Suppose the intersection number a1 = 0, a2 6= 0 in Γ. We prove the following (i)-(ii) are equivalent. (i) Γ is Q-polynomial and con...
متن کاملEdge-distance-regular graphs are distance-regular
A graph is edge-distance-regular when it is distance-regular around each of its edges and it has the same intersection numbers for any edge taken as a root. In this paper we give some (combinatorial and algebraic) proofs of the fact that every edge-distance-regular graph Γ is distance-regular and homogeneous. More precisely, Γ is edge-distance-regular if and only if it is bipartite distance-reg...
متن کاملShilla distance-regular graphs
A Shilla distance-regular graph Γ (say with valency k) is a distance-regular graph with diameter 3 such that its second largest eigenvalue equals to a3. We will show that a3 divides k for a Shilla distance-regular graph Γ, and for Γ we define b = b(Γ) := k a3 . In this paper we will show that there are finitely many Shilla distance-regular graphs Γ with fixed b(Γ) ≥ 2. Also, we will classify Sh...
متن کاملDistance mean-regular graphs
We introduce the concept of distance mean-regular graph, which can be seen as a generalization of both vertex-transitive and distance-regular graphs. A graph Γ = (V,E) with diameter D is distance meanregular when, for given u ∈ V , the averages of the intersection numbers ai(u, v), bi(u, v), and ci(u, v) (defined as usual), computed over all vertices v at distance i = 0, 1, . . . , D from u, do...
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: European Journal of Combinatorics
سال: 1995
ISSN: 0195-6698
DOI: 10.1016/0195-6698(95)90020-9