An inequality between intersection numbers of a distance-regular graph

نویسندگان

چکیده

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A relationship between the diameter and the intersection number c 2 for a distance-regular graph

In this paper we will look at the relationship between the intersection number c2 and its diameter for a distance-regular graph. And also, we give some tools to show that a distance-regular graph with large c2 is bipartite, and a tool to show that if kD is too small then the distance-regular graph has to be antipodal.

متن کامل

An Inequality Involving the Local Eigenvalues of a Distance-Regular Graph

Let denote a distance-regular graph with diameter D ≥ 3, valency k, and intersection numbers ai , bi , ci . Let X denote the vertex set of and fix x ∈ X . Let denote the vertex-subgraph of induced on the set of vertices in X adjacent x . Observe has k vertices and is regular with valency a1. Let η1 ≥ η2 ≥ · · · ≥ ηk denote the eigenvalues of and observe η1 = a1. Let denote the set of distinct s...

متن کامل

Subgraphs Graph in a Distance-regular Graph

Let Γ denote a D-bounded distance-regular graph, where D ≥ 3 is the diameter of Γ. For 0 ≤ s ≤ D − 3 and a weak-geodetically closed subgraph ∆ of Γ with diameter s, define a graph G(∆) whose vertex set is the collection of all weak-geodetically closed subgraphs of diameter s+2 containing ∆, and vertex Ω is adjacent to vertex Ω′ in G if and only if Ω∩Ω′ as a subgraph of Γ has diameter s+1. We sh...

متن کامل

A Questionable Distance-Regular Graph

In this paper, we introduce distance-regular graphs and develop the intersection algebra for these graphs which is based upon its intersection numbers. We discuss results following from the definition of the intersection algebra. We investigate two examples of distance-regular graphs and show how these results apply. Finally, we introduce parameters that determine intersection numbers. We inves...

متن کامل

The Nonexistence of a Distance-Regular Graph with Intersection Array {22, 16, 5;1, 2, 20}

We prove that a distance-regular graph with intersection array {22, 16, 5; 1, 2, 20} does not exist. To prove this, we assume that such a graph exists and derive some combinatorial properties of its local graph. Then we construct a partial linear space from the local graph to display the contradiction.

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

ژورنال

عنوان ژورنال: Journal of Combinatorial Theory, Series B

سال: 1987

ISSN: 0095-8956

DOI: 10.1016/0095-8956(87)90012-8