منابع مشابه
On k-Walk-Regular Graphs
Considering a connected graph G with diameter D, we say that it is k-walk-regular, for a given integer k (0 ≤ k ≤ D), if the number of walks of length l between vertices u and v only depends on the distance between them, provided that this distance does not exceed k. Thus, for k = 0, this definition coincides with that of walk-regular graph, where the number of cycles of length l rooted at a gi...
متن کاملOn t-Cliques in k-Walk-Regular Graphs
A graph is walk-regular if the number of cycles of length ` rooted at a given vertex is a constant through all the vertices. For a walk-regular graph G with d + 1 different eigenvalues and spectrally maximum diameter D = d, we study the geometry of its d-cliques, that is, the sets of vertices which are mutually at distance d. When these vertices are projected onto an eigenspace of its adjacency...
متن کاملSpectral and Geometric Properties of k-Walk-Regular Graphs
Let us consider a connected graph G with diameter D. For a given integer k between 0 and D, we say that G is k-walk-regular if the number of walks of length between vertices u, v only depends on the distance between u and v, provided that such a distance does not exceed k. Thus, in particular, a 0-walk-regular graph is the same as a walk-regular graph, where the number of cycles of length roote...
متن کاملThe Geometry of t-Cliques in k-Walk-Regular Graphs
A graph is walk-regular if the number of cycles of length l rooted at a given vertex is a constant through all the vertices. For a walk-regular graph G with d+1 different eigenvalues and spectrally maximum diameter D = d, we study the geometry of its d-cliques, that is, the sets of vertices which are mutually at distance d. When these vertices are projected onto an eigenspace of its adjacency m...
متن کاملWalk-regular divisible design graphs
A divisible design graph (DDG for short) is a graph whose adjacency matrix is the incidence matrix of a divisible design. DDGs were introduced by Kharaghani, Meulenberg and the second author as a generalization of (v, k, λ)-graphs. It turns out that most (but not all) of the known examples of DDGs are walk-regular. In this paper we present an easy criterion for this to happen. In several cases ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2009
ISSN: 1077-8926
DOI: 10.37236/136