Strong matching preclusion of (n,k)-star graphs

Strong Matching Preclusion for Augmented Butterfly Networks

“…Park and Ihm [8] also studied the problem of strong matching preclusion under the condition that no isolated vertex is created as a result of faults, and established the conditional strong matching preclusion number for the class of restricted hypercube-like graphs, which include most non bipartite hypercube-like networks found in the literature. SMP numbers of augmented cubes, arrangement graphs, alternating group graphs and split-star, pancake graphs, 2 -matching composition networks, k -ary n cubes, n-dimensional torus networks, k-composition networks are also investigated; see [1,[9][10][11][12][13][14].…”

Super edge-connectivity and matching preclusion of data center networks

“…Until now, the matching preclusion number of numerous networks were calculated and the corresponding optimal solutions were obtained, such as the complete graph, the complete bipartite graph and the hypercube [6], Cayley graphs generated by 2-trees and hyper Petersen networks [10], Cayley graphs generalized by transpositions and (n, k)-star graphs [11], restricted HL-graphs and recursive circulant G(2 m , 4) [31], tori and related Cartesian products [12], (n, k)-bubble-sort graphs [13], balanced hypercubes [27], burnt pancake graphs [22], k-ary n-cubes [35], cube-connected cycles [25], vertex-transitive graphs [24], n-dimensional torus [23], binary de Bruijn graphs [26] and n-grid graphs [17]. For the conditional matching preclusion problem, it is solved for the complete graph, the complete bipartite graph and the hypercube [6], arrangement graphs [14], alternating group graphs and split-stars [15], Cayley graphs generated by 2-trees and the hyper Petersen networks [10], Cayley graphs generalized by transpositions and (n, k)-star graphs [11], burnt pancake graphs [8,22], balanced hypercubes [27], restricted HL-graphs and recursive circulant G(2 m , 4) [31], k-ary n-cubes [35], hypercube-like graphs [32] and cube-connected cycles [25].…”

A Complete Classification of Which (n, k)-Star Graphs are Cayley Graphs

“…There has been much research on the class of (n, k)-star graphs studying embeddings, broadcasting, Hamiltonicity and surface area as well as their applicability in theoretical computer science. Recent papers (within the past 3 years) include [4,5,7,8,10,13,17,20,23,28,29]. The first major result on Hamiltonicity was given in [17], which proves that (n, k)-star graphs are Hamiltonian; in fact, an (n, k)-star graph remains Hamiltonian if n − 3 vertices and/or edges are deleted.…”

“…• (n, k) is one of the following sporadic cases: (n, k) = (9, 4), (9,6), (11,4), (12,5), (33, 4), or (33, 30).…”

“…Even though this minimum condition on r is not stated in[11, Theorem 5.2B], a Remark after Theorem 5.2B mentions that "the group are listed only with the minimum r for which they satisfy the hypotheses of the theorem". Without the minimum condition, there could be more exceptional cases such as(6,3,6),(6,3,12),(8,4, 30).…”