Pseudo-distance-regularized graphs are distance-regular or distance-biregular
نویسندگان
چکیده
منابع مشابه
Edge-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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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....
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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...
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We construct two families of distance-regular graphs, namely the subgraph of the dual polar graph of type B3(q) induced on the vertices far from a fixed point, and the subgraph of the dual polar graph of type D4(q) induced on the vertices far from a fixed edge. The latter is the extended bipartite double of the former.
متن کاملEdge-distance-regular graphs
Edge-distance-regularity is a concept recently introduced by the authors which is similar to that of distance-regularity, but now the graph is seen from each of its edges instead of from its vertices. More precisely, a graph Γ with adjacency matrix A is edge-distance-regular when it is distance-regular around each of its edges and with the same intersection numbers for any edge taken as a root....
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2012
ISSN: 0024-3795
DOI: 10.1016/j.laa.2012.07.019