Browsing by Author "Pan, Yeh-jong"

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3-bounded property in a triangle-free distance-regular graph
(2008-10-01)
Pan, Yeh-jong
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Weng, Chih-wen
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應用數學系
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Department of Applied Mathematics
Let Gamma denote a distance-regular graph with classical parameters (D, b, alpha, beta) and D >= 3. Assume the intersection numbers a(1) = 0 and a(2) not equal 0. We show that Gamma is 3-bounded in the sense of the article [C. Weng, D-bounded distance-regular graphs, European Journal of Combinatorics 18 (1997) 211-229]. (c) 2007 Elsevier Ltd. All rights reserved.
A note on triangle-free distance-regular graphs with a(2) not equal 0
(2009-01-01)
Pan, Yeh-jong
;
Weng, Chih-wen
;
應用數學系
;
Department of Applied Mathematics
Let Gamma denote a distance-regular graph with classical parameters (D, b, alpha, beta) and D >= 3. Assume the intersection numbers a(1) = 0 and a(2) not equal 0. We show that the intersection number c(2) is either 1 or 2, and if c(2) = 1, then (b, alpha, beta) = (-2, -2, ((-2)(D+l) - 1)/3). (C) 2008 Elsevier Inc. All rights reserved.
Nonexistence of a Class of Distance-regular Graphs
(2015-06-03)
Huang, Yu-pei
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Pan, Yeh-jong
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Weng, Chih-wen
;
應用數學系
;
Department of Applied Mathematics
Let Gamma denote a distance-regular graph with diameter D >= 3 and intersection numbers a(1) = 0, a(2) not equal 0, and c(2) = 1. We show a connection between the d-bounded property and the nonexistence of parallelograms of any length up to d + 1. Assume further that Gamma is with classical parameters (D, b, alpha, beta), Pan and Weng (2009) showed that (b, alpha, beta) = (-2, 2, ((-2)(D+1) -1)/3). Under the assumption D >= 4, we exclude this class of graphs by an application of the above connection.
Triangle-free distance-regular graphs
(2008-02-01)
Pan, Yeh-jong
;
Lu, Min-hsin
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Weng, Chih-wen
;
應用數學系
;
Department of Applied Mathematics
Let Gamma denote a distance-regular graph with diameter d >= 3. By a parallelogram of length 3, we mean a 4-tuple xyzw consisting of vertices of Gamma such that partial derivative(x,y)=partial derivative(z,w)=1, partial derivative(x,z)=3, and partial derivative(x,w)=partial derivative(y,w)=partial derivative(y,z)=2, where partial derivative denotes the path-length distance function. Assume that Gamma has intersection numbers a(1)=0 and a(2)not equal 0. We prove that the following (i) and (ii) are equivalent. (i) Gamma is Q-polynomial and contains no parallelograms of length 3; (ii) Gamma has classical parameters (d,b,alpha,beta) with b <-1. Furthermore, suppose that (i) and (ii) hold. We show that each of b(b+1)(2)(b+2)/c (2), (b-2)(b-1)b(b+1)/(2+2b-c (2)) is an integer and that c (2)<= b(b+1). This upper bound for c (2) is optimal, since the Hermitian forms graph Her(2)(d) is a triangle-free distance-regular graph that satisfies c (2)=b(b+1).