Results 1  10
of
378,750
A characterization of Qpolynomial distanceregular graphs
, 2009
"... We obtain the following characterization of Qpolynomial distanceregular graphs. Let Γ denote a distanceregular graph with diameter d ≥ 3. Let E denote a minimal idempotent of Γ which is not the trivial idempotent E0. Let {θ ∗ i}di=0 denote the dual eigenvalue sequence for E. We show that E is Qp ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We obtain the following characterization of Qpolynomial distanceregular graphs. Let Γ denote a distanceregular graph with diameter d ≥ 3. Let E denote a minimal idempotent of Γ which is not the trivial idempotent E0. Let {θ ∗ i}di=0 denote the dual eigenvalue sequence for E. We show that E is Qpolynomial
Homotopy in Qpolynomial distanceregular graphs
, 2000
"... Let denote a Qpolynomial distanceregular graph with diameter d ¿ 3. We show that if the valency is at least three, then the intersection number p 3 12 is at least two; consequently the girth is at most six. We then consider a condition on the dual eigenvalues of that must hold if is the quotient o ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Let denote a Qpolynomial distanceregular graph with diameter d ¿ 3. We show that if the valency is at least three, then the intersection number p 3 12 is at least two; consequently the girth is at most six. We then consider a condition on the dual eigenvalues of that must hold if is the quotient
Almostbipartite distanceregular graphs with the Qpolynomial property
, 2004
"... Let Γ denote a Qpolynomial distanceregular graph with diameter D ≥ 4. Assume that the intersection numbers of Γ satisfy ai = 0 for 0 ≤ i ≤ D − 1 and aD ̸ = 0. We show that Γ is a polygon, a folded cube, or an Odd graph. ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Let Γ denote a Qpolynomial distanceregular graph with diameter D ≥ 4. Assume that the intersection numbers of Γ satisfy ai = 0 for 0 ≤ i ≤ D − 1 and aD ̸ = 0. We show that Γ is a polygon, a folded cube, or an Odd graph.
ON BIPARTITE QPOLYNOMIAL DISTANCEREGULAR GRAPHS
, 2005
"... Let Γ denote a bipartite Qpolynomial distanceregular graph with vertex set X, diameter d ≥ 3 and valency k ≥ 3. Let R X denote the vector space over R consisting of column vectors with entries in R and rows indexed by X. For z ∈ X, let ˆz denote the vector in R X with a 1 in the zcoordinate, and ..."
Abstract

Cited by 11 (1 self)
 Add to MetaCart
Let Γ denote a bipartite Qpolynomial distanceregular graph with vertex set X, diameter d ≥ 3 and valency k ≥ 3. Let R X denote the vector space over R consisting of column vectors with entries in R and rows indexed by X. For z ∈ X, let ˆz denote the vector in R X with a 1 in the z
Tight DistanceRegular Graphs
"... We consider a distanceregular graph \Gamma with diameter d 3 and eigenvalues k = ..."
Abstract

Cited by 12 (5 self)
 Add to MetaCart
We consider a distanceregular graph \Gamma with diameter d 3 and eigenvalues k =
The displacement and split decompositions for a Qpolynomial distanceregular graph
, 2003
"... ..."
Algebraic characterizations of distanceregular graphs
 DISCRETE MATH
, 2001
"... We survey some old and some new characterizations of distanceregular graphs, which depend on information retrieved from their adjacency matrix. In particular, it is shown that a regular graph with d+ 1 distinct eigenvalues is distanceregular if and only if a numeric equality, involving only the sp ..."
Abstract

Cited by 25 (16 self)
 Add to MetaCart
We survey some old and some new characterizations of distanceregular graphs, which depend on information retrieved from their adjacency matrix. In particular, it is shown that a regular graph with d+ 1 distinct eigenvalues is distanceregular if and only if a numeric equality, involving only
DistanceRegularity and the Spectrum of Graphs
, 1996
"... We deal with the question: Can one see from the spectrum of a graph F whether it is distanceregular or not? Up till now the answer has not been known when F has precisely four distinct eigenvalues (the diameter 3 case). We show that in this case the answer is negative. We also give positive answers ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
We deal with the question: Can one see from the spectrum of a graph F whether it is distanceregular or not? Up till now the answer has not been known when F has precisely four distinct eigenvalues (the diameter 3 case). We show that in this case the answer is negative. We also give positive
Results 1  10
of
378,750