In this paper, we consider the ring embedding problem in faulty star graphs. Our embedding is based on the path transition scheme and node borrow technique in the ring of 4-dimensional substars with evenly distributed faults. Let Sn be the n-dimensional star graph having n! nodes. We will show that a ring of length n! - 2f can be found in Sn when the number of faulty nodes f is at most n-3. In the worst case, the loss of 2f nodes in the size of fault-free ring is inevitable because the star graph is bipartite. In addition, this result is superior to the best previous result that constructs the ring of length n! - 4f under the same fault condition. Moreover, by extending this result into the star graph with both node and edge faults simultaneously, we can find the fault-free ring of length n! - 2 fn in Sn when it contains fn faulty nodes and fe faulty edges such that fn + fe
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Jung-Hwan CHANG, Chan-Su SHIN, Kyung-Yong CHWA, "Ring Embedding in Faulty Star Graphs" in IEICE TRANSACTIONS on Fundamentals,
vol. E82-A, no. 9, pp. 1953-1964, September 1999, doi: .
Abstract: In this paper, we consider the ring embedding problem in faulty star graphs. Our embedding is based on the path transition scheme and node borrow technique in the ring of 4-dimensional substars with evenly distributed faults. Let Sn be the n-dimensional star graph having n! nodes. We will show that a ring of length n! - 2f can be found in Sn when the number of faulty nodes f is at most n-3. In the worst case, the loss of 2f nodes in the size of fault-free ring is inevitable because the star graph is bipartite. In addition, this result is superior to the best previous result that constructs the ring of length n! - 4f under the same fault condition. Moreover, by extending this result into the star graph with both node and edge faults simultaneously, we can find the fault-free ring of length n! - 2 fn in Sn when it contains fn faulty nodes and fe faulty edges such that fn + fe
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_9_1953/_p
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@ARTICLE{e82-a_9_1953,
author={Jung-Hwan CHANG, Chan-Su SHIN, Kyung-Yong CHWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Ring Embedding in Faulty Star Graphs},
year={1999},
volume={E82-A},
number={9},
pages={1953-1964},
abstract={In this paper, we consider the ring embedding problem in faulty star graphs. Our embedding is based on the path transition scheme and node borrow technique in the ring of 4-dimensional substars with evenly distributed faults. Let Sn be the n-dimensional star graph having n! nodes. We will show that a ring of length n! - 2f can be found in Sn when the number of faulty nodes f is at most n-3. In the worst case, the loss of 2f nodes in the size of fault-free ring is inevitable because the star graph is bipartite. In addition, this result is superior to the best previous result that constructs the ring of length n! - 4f under the same fault condition. Moreover, by extending this result into the star graph with both node and edge faults simultaneously, we can find the fault-free ring of length n! - 2 fn in Sn when it contains fn faulty nodes and fe faulty edges such that fn + fe
keywords={},
doi={},
ISSN={},
month={September},}
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TY - JOUR
TI - Ring Embedding in Faulty Star Graphs
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1953
EP - 1964
AU - Jung-Hwan CHANG
AU - Chan-Su SHIN
AU - Kyung-Yong CHWA
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E82-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 1999
AB - In this paper, we consider the ring embedding problem in faulty star graphs. Our embedding is based on the path transition scheme and node borrow technique in the ring of 4-dimensional substars with evenly distributed faults. Let Sn be the n-dimensional star graph having n! nodes. We will show that a ring of length n! - 2f can be found in Sn when the number of faulty nodes f is at most n-3. In the worst case, the loss of 2f nodes in the size of fault-free ring is inevitable because the star graph is bipartite. In addition, this result is superior to the best previous result that constructs the ring of length n! - 4f under the same fault condition. Moreover, by extending this result into the star graph with both node and edge faults simultaneously, we can find the fault-free ring of length n! - 2 fn in Sn when it contains fn faulty nodes and fe faulty edges such that fn + fe
ER -