The Distance-Regular Graphs of Valency Four

نویسنده

  • A. E. BROUWER
چکیده

We show that each distance-regular graph of valency four has known parameters.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Se p 20 09 There are only finitely many distance - regular graphs of fixed valency greater than two

There are only finitely many distance-regular graphs of fixed valency greater than two Abstract In this paper we prove the Bannai-Ito conjecture, namely that there are only finitely many distance-regular graphs of fixed valency greater than two.

متن کامل

Distance-Regular Graphs of Valency 6 and a1 = 1

We give a complete classification of distance-regular graphs of valency 6 and a1 = 1.

متن کامل

On Subgraphs in Distance-Regular Graphs

Terwilliger [15] has given the diameter bound d < (s 1)(k 1) + 1 for distance-regular graphs with girth 2s and valency k. We show that the only distance-regular graphs with even girth which reach this bound are the hypercubes and the doubled Odd graphs. Also we improve this bound for bipartite distance-regular graphs. Weichsel [17] conjectures that the only distance-regular subgraphs of a hyper...

متن کامل

Distance-regular graphs with an eigenvalue

It is known that bipartite distance-regular graphs with diameter D > 3, valency k > 3, intersection number c2 > 2 and eigenvalues k = θ0 > θ1 > · · · > θD satisfy θ1 6 k− 2 and thus θD−1 > 2− k. In this paper we classify non-complete distanceregular graphs with valency k > 2, intersection number c2 > 2 and an eigenvalue θ satisfying −k < θ 6 2 − k. Moreover, we give a lower bound for valency k ...

متن کامل

Distance-Regular Graphs with a Relatively Small Eigenvalue Multiplicity

Godsil showed that if Γ is a distance-regular graph with diameter D > 3 and valency k > 3, and θ is an eigenvalue of Γ with multiplicity m > 2, then k 6 (m+2)(m−1) 2 . In this paper we will give a refined statement of this result. We show that if Γ is a distance-regular graph with diameter D > 3, valency k > 2 and an eigenvalue θ with multiplicity m > 2, such that k is close to (m+2)(m−1) 2 , t...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1999