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g-Good-Neighbor Diagnosability of Arrangement Graphs under the PMC Model and MM* Model
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Information 2019, 10(1), 21; https://doi.org/10.3390/info10010021

The g-Good-Neighbor Diagnosability of Bubble-Sort Graphs under Preparata, Metze, and Chien’s (PMC) Model and Maeng and Malek’s (MM)* Model

College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
*
Author to whom correspondence should be addressed.
Received: 2 December 2018 / Revised: 22 December 2018 / Accepted: 4 January 2019 / Published: 10 January 2019
(This article belongs to the Special Issue Graphs for Smart Communications Systems)
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Abstract

Diagnosability of a multiprocessor system is an important topic of study. A measure for fault diagnosis of the system restrains that every fault-free node has at least g fault-free neighbor vertices, which is called the g-good-neighbor diagnosability of the system. As a famous topology structure of interconnection networks, the n-dimensional bubble-sort graph B n has many good properties. In this paper, we prove that (1) the 1-good-neighbor diagnosability of B n is 2 n 3 under Preparata, Metze, and Chien’s (PMC) model for n 4 and Maeng and Malek’s (MM) model for n 5 ; (2) the 2-good-neighbor diagnosability of B n is 4 n 9 under the PMC model and the MM model for n 4 ; (3) the 3-good-neighbor diagnosability of B n is 8 n 25 under the PMC model and the MM model for n 7 . View Full-Text
Keywords: interconnection network; graph; diagnosability; PMC model; MM* model; bubble-sort graph interconnection network; graph; diagnosability; PMC model; MM* model; bubble-sort graph
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Wang, S.; Wang, Z. The g-Good-Neighbor Diagnosability of Bubble-Sort Graphs under Preparata, Metze, and Chien’s (PMC) Model and Maeng and Malek’s (MM)* Model. Information 2019, 10, 21.

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