Browsing by Author "Shiue, Chin-Lin"

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A note on optimal pebbling of hypercubes
(2013-05-01)
Fu, Hung-Lin
;
Huang, Kuo-Ching
;
Shiue, Chin-Lin
;
應用數學系
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Department of Applied Mathematics
A pebbling move consists of removing two pebbles from one vertex and then placing one pebble at an adjacent vertex. If a distribution delta of pebbles lets us move at least one pebble to each vertex by applying pebbling moves repeatedly(if necessary), then delta is called a pebbling of G. The optimal pebbling number f'(G) of G is the minimum number of pebbles used in a pebbling of G. In this paper, we improve the known upper bound for the optimal pebbling number of the hypercubes Q (n) . Mainly, we prove for large n, by a probabilistic argument.
alpha-labeling number of trees
(2006-12-28)
Shiue, Chin-Lin
;
Fu, Hung-Lin
;
應用數學系
;
Department of Applied Mathematics
In this paper, we prove that the alpha-labeling number of trees T, T-alpha <= [r/2] n where n = vertical bar E(T)vertical bar and r is the radius of T. This improves the known result T-alpha <= e(O(root nlogn)) tremendously and this upper bound is very close to the upper bound T-alpha <= n conjectured by Snevily. Moreover, we prove that a tree with n edges and radius r decomposes K-1 for some t <= (r + 1)n(2) + 1. (c) 2006 Elsevier B.V. All rights reserved.
The IC-indices of complete bipartite graphs
(2008-03-12)
Shiue, Chin-Lin
;
Fu, Hung-Lin
;
應用數學系
;
Department of Applied Mathematics
Let G be a connected graph, and let f be a function mapping V(G) into N. We define f(H) = Sigma(nu is an element of V(H)) f(nu) for each subgraph H of G. The function f is called an IC-coloring of G if for each integer k in the set {1, 2, ... , f(G)} there exists and (induced) connected subgraph H of G such that f(H) = k, and the IC-index of G, M(G), is the maximum value of f(G) where f is an IC-coloring of G. In this paper, we show that M(K-m,K-n) = 3.2(m+n-2)-2(m-2)+2 for each complete bipartite graph K-m,K-n, 2 <= m <= n.
THE OPTIMAL PEBBLING NUMBER OF THE CATERPILLAR
(2009-04-01)
Shiue, Chin-Lin
;
Fu, Hung-Lin
;
應用數學系
;
Department of Applied Mathematics
Let G be a simple graph. If we place p pebbles on the vertices of G, then a pebbling move is taking two pebbles off one vertex and then placing one on an adjacent vertex. The optimal pebbling number of G, f'(G), is the least positive integer p such that p pebbles are placed suitably on vertices of G and for any target vertex nu of G, we can move one pebble to nu by a sequence of pebbling moves. In this paper, we find the optimal pebbling number of the caterpillars.
Trees Which Admit No alpha-labelings
(2012-01-01)
Shiue, Chin-Lin
;
Lu, Hui-Chuan
;
應用數學系
;
Department of Applied Mathematics
In this paper, we study the existence of alpha-labelings for trees by means of particular (0, 1)-matrices called alpha-labeling matrices. It is shown that each cornet S(k,q) admits no alpha-labelings whenever k > 4(q - 1) and q >= 2. We also give the sufficient conditions for the nonexistence of alpha-labelings for trees of diameter at most six. This extends a result of Rosa's. As a consequence, we prove that S(k,3) has an alpha-labeling if and only if k <= 4.