Fault diagnosability of regular graphs

Authors

Mei-Mei Gu, Department of Science and Technology, China University of Political Science and Law, Beijing 102249, ChinaFollow
Rong-Xia Hao, Department of Mathematics, Beijing Jiaotong University, Beijing 100044, ChinaFollow
Eddie Cheng, Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USAFollow

Abstract

An interconnection network's diagnosability is an important measure of its self-diagnostic capability. In 2012, Peng et al. proposed a measure for fault diagnosis of the network, namely, the h-good-neighbor conditional diagnosability, which requires that every fault-free node has at least h fault-free neighbors. There are two well-known diagnostic models, PMC model and MM* model. The h-good-neighbor diagnosability under the PMC (resp. MM*) model of a graph G, denoted by t_h^PMC(G) (resp. t_h^MM*(G)), is the maximum value of t such that G is h-good-neighbor t-diagnosable under the PMC (resp. MM*) model. In this paper, we study the 2-good-neighbor diagnosability of some general k-regular k-connected graphs G under the PMC model and the MM* model. The main result t₂^PMC(G)=t₂^MM*}(G)=g(k-1)-1 with some acceptable conditions is obtained, where g is the girth of G. Furthermore, the following new results under the two models are obtained: t₂^PMC(HS_n)=t₂^MM*}(HS_n)=4n-5 for the hierarchical star network HS_n, t₂^PMC(S_n²)=t₂^MM*(S_n²)=6n-13 for the split-star networks S_n² and t₂^PMC}(Γ_n(Δ))=t₂^MM*}(Γ_n(Δ))=6n-16 for the Cayley graph generated by the 2-tree Γ_n(Δ).

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Gu, Mei-Mei; Hao, Rong-Xia; and Cheng, Eddie (2020) "Fault diagnosability of regular graphs," Theory and Applications of Graphs: Vol. 7: Iss. 2, Article 4.
DOI: 10.20429/tag.2020.070204
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol7/iss2/4