منابع مشابه
Locally Pseudo-Distance-Regular Graphs
The concept of local pseudo-distance-regularity, introduced in this paper, can be thought of as a natural generalization of distance-regularity for non-regular graphs. Intuitively speaking, such a concept is related to the regularity of graph 1 when it is seen from a given vertex. The price to be paid for speaking about a kind of distance-regularity in the non-regular case seems to be locality....
متن کاملFrom Local Adjacency Polynomials to Locally Pseudo-Distance-Regular Graphs
The local adjacency polynomials can be thought of as a generalization, for all graphs, of (the sums of ) the distance polynomials of distance-regular graphs. The term ``local'' here means that we ``see'' the graph from a given vertex, and it is the price we must pay for speaking of a kind of distance-regularity when the graph is not regular. It is shown that when the value at * (the maximum eig...
متن کاملPseudo 1-homogeneous distance-regular graphs
Let be a distance-regular graph of diameter d ≥ 2 and a1 = 0. Let θ be a real number. A pseudo cosine sequence for θ is a sequence of real numbers σ0, . . . , σd such that σ0 = 1 and ciσi−1 + aiσi + biσi+1 = θσi for all i ∈ {0, . . . , d−1}. Furthermore, a pseudo primitive idempotent for θ is Eθ = s ∑di=0 σiAi , where s is any nonzero scalar. Let v̂ be the characteristic vector of a vertex v ∈ V...
متن کاملDistance-regular graphs, pseudo primitive idempotents, and the Terwilliger algebra
Let Γ denote a distance-regular graph with diameter D ≥ 3, intersection numbers ai, bi, ci and Bose-Mesner algebra M. For θ ∈ C ∪∞ we define a 1 dimensional subspace of M which we call M(θ). If θ ∈ C then M(θ) consists of those Y in M such that (A−θI)Y ∈ CAD, where A (resp. AD) is the adjacency matrix (resp. Dth distance matrix) of Γ. If θ = ∞ then M(θ) = CAD. By a pseudo primitive idempotent f...
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...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1996
ISSN: 0095-8956
DOI: 10.1006/jctb.1996.0063