An interconnection network\u27s 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 {\it h-good-neighbor diagnosability} under the PMC (resp. MM*) model of a graph G, denoted by thPMCβ(G) (resp. thMMββ(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 t2PMCβ(G)=t2MMββ(G)=g(kβ1)β1 with some acceptable conditions is obtained, where g is the girth of G. Furthermore, the following new results under the two models are obtained: t2PMCβ(HSnβ)=t2MMββ(HSnβ)=4nβ5 for the hierarchical star network HSnβ, t2PMCβ(Sn2β)=t2MMββ(Sn2β)=6nβ13 for the split-star networks Sn2β and t2PMCβ(Ξnβ(Ξ))=t2MMββ(Ξnβ(Ξ))=6nβ16 for the Cayley graph generated by the 2-tree Ξnβ(Ξ)
The g-extraconnectivityΞΊgβ(G) of a connected graph G is
the minimum cardinality of a set of vertices, if it exists, whose deletion
makes G disconnected and leaves each remaining component with more than g
vertices, where g is a non-negative integer. The strongproductG1ββ G2β of graphs G1β and G2β is the graph with vertex set V(G1ββ G2β)=V(G1β)ΓV(G2β), where two distinct vertices (x1β,y1β),(x2β,y2β)βV(G1β)ΓV(G2β) are adjacent in G1ββ G2β if and only if x1β=x2β and y1βy2ββE(G2β) or y1β=y2β
and x1βx2ββE(G1β) or x1βx2ββE(G1β) and y1βy2ββE(G2β). In this paper, we give the gΒ (β€3)-extraconnectivity of
G1ββ G2β, where Giβ is a maximally connected kiβΒ (β₯2)-regular graph for i=1,2. As a byproduct, we get gΒ (β€3)-extra
conditional fault-diagnosability of G1ββ G2β under PMC model