Browsing by Author "Kuo, Jyhmin"

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ON NEAR RELATIVE PRIME NUMBER IN A SEQUENCE OF POSITIVE INTEGERS
(2010-02-01)
Kuo, Jyhmin
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Fu, Hung-Lin
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應用數學系
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Department of Applied Mathematics
Let A be a sequence of positive integers. An element alpha of A is called an s-near relative prime number (s-near relprime in short) if alpha is coprime to any distinct element in A except exactly s elements of A. In this paper, we study the existence of an arithmetic sequence with no 1-near relprimes.
On the decycling number of generalized Kautz digraphs
(2015-02-01)
Lien, Min-Yun
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Kuo, Jyhmin
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Fu, Hung-Lin
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應用數學系
;
Department of Applied Mathematics
For n > d >= 2, the generalized Kautz digraph G(K)(d, n) is defined by congruence equations as follows: V(G(K)(d, n)) = {0, 1, 2, . . . , n - 1} and A (G(K)( (d, n)) = {(x, y)vertical bar y equivalent to -dx - i (mod n), 1 <= i <= d}. A set of vertices of a graph whose removal leaves an acyclic graph is called a decycling set of the graph. The minimum size of a decycling set of a graph G is referred to as the decycling number of G. Let f(d, n) be the decycling number of the generalized Kautz digraph G(K)(d, n). In this paper, we study f (d, n) for all n >= d >= 2. As a consequence, we obtain the upper bound of f(d, n) as follows: f(d, n) <= (1/2 - d-1/2d(2))n + d/2(d - t + 5) - 2, where n equivalent to t (mod(d + 1)). (C) 2014 Elsevier B.V. All rights reserved.
On the Diameter of the Generalized Graphs UG(B)(n, m), n(2) < m <= n(3)
(2008-12-01)
Kuo, Jyhmin
;
Fu, Hung-Lin
;
應用數學系
;
Department of Applied Mathematics
The generalized de Bruijn digraph G(B)(n, m) is the digraph (V, A) where V = {0, 1, ..., m-1) and (i, j) is an element of A if and only if j equivalent to in + alpha (mod m) for some alpha is an element of {0, 1, 2, ..., n-1}. By replacing each arc of G(B)(n, m) with an undirected edge and eliminating loops and multi-edges, we obtain the generalized undirected de Bruijn graph UG(B)(n, m). In this article, we prove that when 2n(2) <= m <= n(3) the diameter of UG(B)(n, m) is equal to 3. We also show that for pairs (n, m) where n(2) < m < 2n(2) the diameter of UG(B) (n, m) can be 2 or 3. (C) 2008 Wiley Periodicals, Inc. NETWORKS, Vol. 52(4), 180-182 2008
On the Diameter of the Generalized Undirected De Bruijn Graphs
(2012-07-01)
Kuo, Jyhmin
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Fu, Hung-Lin
;
應用數學系
;
Department of Applied Mathematics
The generalized de Bruijn digraph denoted by G(B)(n, m) is the digraph (V, A) where V = {0, 1, . . . , m - 1} and (i, j) is an element of A if and only if j equivalent to ni + alpha (mod m) for some alpha is an element of {0, 1, . . . , n - 1}. By replacing each arc of G(B)(n, m) with an undirected edge and eliminating loops and multi-edges, we obtain a generalized undirected de Bruijn graph UG(B)(n, m). In this paper, we prove that the diameter of UG(B)(n, m) is equal to 3 whenever n >= 2 and n(2) + (root 5+1/2)n <= m <= 2n(2).
The Absorbant Number of Generalized de Bruijn Digraphs
(2015-01-01)
Kuo, Jyhmin
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Fu, Hung-Lin
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應用數學系
;
Department of Applied Mathematics
Let D = (V, A) be a digraph with the vertex set V and the arc set A. An absorbant of D is a set S subset of V such that for each v is an element of VS, O(v) boolean AND S not equal empty set where O(v) is the out-neighborhood of v. The absorbant number of D, denoted by gamma(a)(D), is defined as the minimum cardinality of an absorbant of D. The generalized de Bruijn digraph G(B)(n,d) is a digraph with the vertex set V(G(B)(n, d)) = {0, 1, 2, ..., n - 1} and the arc set A(G(B)(n, d)) = {(x, y)vertical bar y equivalent to dx + i (mod n),0 <= i < d}. In this paper, we determine gamma(a)(G(B)(n, d)) for all d <= n <= 4d.
Wide diameters of de Bruijn graphs
(2007-10-01)
Kuo, Jyhmin
;
Fu, Hung-Lin
;
應用數學系
;
Department of Applied Mathematics
The wide diameter of a graph is an important parameter to measure fault-tolerance of interconnection network. This paper proves that for any two vertices in de Bruijn undirected graph UB(d,n), there are 2d-2 internally disjoint paths of length at most 2n+1. Therefore, the (2d-2)-wide diameter of UB(d,n) is not greater than 2n+1.