Title of article :
More balancing for distance-regular graphs
Author/Authors :
Tonejc، نويسنده , , Jernej، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2013
Pages :
12
From page :
195
To page :
206
Abstract :
Let Γ be a distance-regular graph with diameter d ⩾ 2 and let its intersection array be { b 0 , b 1 , … , b d − 1 ; c 1 , … , c d } . For a given eigenvalue θ of Γ and the corresponding minimal idempotent E with the corresponding cosine sequence ω 0 , … , ω d , the following inequality holds c i ( ω 2 + ω i − ( ω 1 + ω i − 1 ) 2 1 + ω i ) + b i − 1 ( ω 2 + ω i − 1 − ( ω 1 + ω i ) 2 1 + ω i − 1 ) ⩾ ( k − θ ) ( ω 1 + ω 2 + ω i − 1 + ω i ) − ( θ + 1 ) ( 1 − ω 2 ) , for any integer i ( 2 ⩽ i ⩽ d ) such that − 1 ∉ { ω i − 1 , ω i } , with equality if and only if for all vertices x , y ∈ V Γ with ∂ ( x , y ) = j + ε , the vectors E ( x + y ) and E ( ∑ z ∈ Γ ( x ) ∩ Γ j − ε ( y ) z + ∑ z ′ ∈ Γ j − ε ( x ) ∩ Γ ( y ) z ′ ) are collinear, where ε = ± 1 2 and j = i − 1 2 . The cases where equality holds are analyzed and new conditions for the vanishing of certain Krein parameters for strongly regular graphs are obtained. In addition, new results for strongly balanced graphs are also presented.
Journal title :
European Journal of Combinatorics
Serial Year :
2013
Journal title :
European Journal of Combinatorics
Record number :
1547258
Link To Document :
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