Two results concerning distance-regular directed graphs
نویسندگان
چکیده
The study of distance-regular directed graphs can be reduced to that of short distance-regular directed graphs. We consider the eigenspaces of the intersection matrix of a short distance-regular directed graph and show that nearly all the eigenvalues are nonreal. Next we show that a nontrivial short distance-regular directed graph is primitive.
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 کاملTwo theorems concerning the Bannai-Ito conjecture
In 1984 Bannai and Ito conjectured that there are finitely many distance-regular graphs with fixed valencies greater than two. In a series of papers, they showed that this is the case for valency 3 and 4, and also for the class of bipartite distance-regular graphs. To prove their result, they used a theorem concerning the intersection array of a triangle-free distance-regular graph, a theorem t...
متن کاملClassification of a class of distance-regular graphs via completely regular codes
The study of P-polynomial association schemes, or distance-regular graphs, and their possible classification is one of the main topics of algebraic combinatorics. One way to approach the issue is through the parameters Pkij which characterize the scheme. The purpose of this paper is to deal with a concrete case. This case is also important in the study of the links between P-polynomial schemes ...
متن کاملDual concepts of almost distance-regularity and the spectral excess theorem
Generally speaking, ‘almost distance-regular’ graphs share some, but not necessarily all, of the regularity properties that characterize distance-regular graphs. In this paper we propose two new dual concepts of almost distance-regularity, thus giving a better understanding of the properties of distance-regular graphs. More precisely, we characterize m-partially distance-regular graphs and j-pu...
متن کاملThe metric dimension of small distance-regular and strongly regular graphs
A resolving set for a graph Γ is a collection of vertices S, chosen so that for each vertex v, the list of distances from v to the members of S uniquely specifies v. The metric dimension of Γ is the smallest size of a resolving set for Γ. A graph is distance-regular if, for any two vertices u, v at each distance i, the number of neighbours of v at each possible distance from u (i.e. i−1, i or i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Australasian J. Combinatorics
دوره 23 شماره
صفحات -
تاریخ انتشار 2001