A relationship between g-good-neighbour conditional diagnosability and g-good-neighbour connectivity in regular graphs

ABSTRACT

In a system , the g-good-neighbour conditional diagnosability is the maximum t such that G is g-good-neighbour t-fault-diagnosable. The g-good-neighbour connectivity is the minimum cardinality of faulty set such that and G−F is disconnected. Under the following three conditions: (1) for any subset , if , then ; (2) there is a subset A of with and such that is a minimum g-good-neighbour faulty set and is a g-good-neighbour faulty set; (3) ; in this paper, we find that holds for k-regular graph G under both PMC model and MM* model, where and g is an integer.

KEYWORDS:

• g-good-neighbour conditional diagnosability
• g-good-neighbour connectivity
• PMC model
• MM* model
• regular graphs

2010 AMS SUBJECT CLASSIFICATIONS:

• 94C12
• 94C15

Acknowledgements

The author is very grateful to the anonymous referees for their valuable suggestions and detailed corrections, which helped improve the original manuscript.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the Fundamental Research Funds for the Central Universities of China [grant number 21616311] and National Natural Science Foundation of China [grant number 11701218].