منابع مشابه
Distance-regular graphs without 4-claws
We determine the distance-regular graphs with diameter at least 3 and c2 ≥ 2 but without induced K1,4-subgraphs.
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 کاملTight Distance-Regular Graphs
We consider a distance regular graph with diameter d and eigenvalues k d We show the intersection numbers a b satisfy k a d k a ka b a We say is tight whenever is not bipartite and equality holds above We charac terize the tight property in a number of ways For example we show is tight if and only if the intersection numbers are given by certain rational expressions involving d independent para...
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: 2019
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2018.02.022