https://ogma.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:37827 G = (V, E). In 2012, a measurement for fault tolerance of the graph was proposed by Peng et al. This measurement is called the g-good-neighbor diagnosability that restrains every fault-free node to contain at least g fault-free neighbors. In 2016, Zhang et al. proposed a new measurement for fault diagnosis of the graph, namely, the g-extra diagnosabil-ity, which restrains that every fault-free component has at least (g+1) fault-free nodes. A fault set F ⊆ V is called a g-good-neighbor faulty set if the degree d(v) ≥ g for every vertex v in G.−F. A g-good-neighbor cut of G is a g-good-neighbor faulty set F such that G−F is disconnected. The minimum cardinality of g-good-neighbor cuts is said to be the g-good-neighbor connectivity of G. A fault set F ⊆ V is called a g-extra faulty set if every component of G−F has at least (g+1) vertices. A g-extra cut of G is a g-extra faulty set F such that G −F is disconnected. The minimum cardinality of g-extra cuts is said to be the g-extra connectivity of G. The g-good-neighbor (extra) diagnosability and g-good-neighbor (extra) connectivity of many well-known graphs have been widely investigated. In this paper, we show the relationship between the g-good-neighbor (extra) diagnosability and g-good-neighbor (extra) connectivity of graphs.]]> Wed 12 May 2021 09:53:36 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:32182 n has many good properties. In this paper, we prove that 2-good-neighbor connectivity of BS_n is 8n - 22 for n ≥ 5 and the 2-good-neighbor connectivity of BS₄ is 8; the 2-good-neighbor diagnosability of BS_n is 8n - 19 under the PMC model and MM* model for n ≥ 5.]]> Wed 09 May 2018 15:40:06 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:44260 n-dimensional bubble-sort star graph BS_n has many good properties. We give some strong connectivity of BS_n, too.]]> Tue 11 Oct 2022 12:49:55 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:32057 n-dimensional bubble-sort star graph BS_n has many good properties. In this paper, we prove that the nature diagnosability of BS_n is 4n - 7 under the PMC model for n ≥ 4, the nature diagnosability of BS_n is n ≥ 4 under the MM* model for n ≥ 5 .]]> Thu 26 Apr 2018 14:24:55 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:35348 Thu 01 Aug 2019 15:36:55 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:24872 n generated by the transposition tree Γ_n has many good properties. In this paper, we give that the 2-good-neighbor diagnosability of CΓ_n under the PMC model and MM⁎ model is g(n−2)−1, where n≥4and g is the girth of CΓ_n.]]> Sat 24 Mar 2018 07:11:20 AEDT ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:32178 et al. proposed the g-extra diagnosability of G, which restrains that every component of G - S has at least (g + 1) vertices. The locally twisted cube LTQ_n is applied widely. In this paper, we show that LTQ_n is tightly (4n-9) super 3-extra connected for n≥6 and the 3-extra diagnosability of LTQ_n under the PMC model and MM* model is 4n - 6 for n≥5 and n≥7, respectively.]]> Mon 23 Sep 2019 12:57:15 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:32988 et al. proposed a new measure for fault tolerance of the system, which is called g-good-neighbour diagnosability that restrains every fault-free node containing at least g fault-free neighbours. As a favourable topology structure of interconnection networks, the Cayley graph CΓ_n generated by the transposition tree Γ_n has many good properties. In this paper, we give that the 1-good-neighbour diagnosability of CΓ_n under the PMC model and MM∗ model is 2_n−3 except the bubble-sort graph B₄ under MM∗ model, where n≥4, and the 1-good-neighbour diagnosability of B₄ under the MM∗ model is 4.]]> Fri 17 Aug 2018 15:44:20 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:43361 CFₙ is 3n−3/2 (3n−3/2) for odd n and 3n−4/2(3n−4/2) for even n; (2) CFₙ is super edge-connected; (3) the matching preclusion number of CFₙ is 3n−3/2 for odd n and 3n−4/2 for even n; (4) the conditional matching preclusion number of CFₙ is 3n – 5 for odd n and n ≥ 3, and 3n – 6 for even n and n ≥ 4.]]> Fri 16 Sep 2022 08:32:44 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:32184 n has many good properties. In this paper, we establish the g-good-neighbor conditional diagnosability of S_n under the PMC model and MM* model.]]> Fri 11 May 2018 13:24:22 AEST ]]>